My vision of an ideal Cyberpunk game would be making the proper desperation atmosphere, creating a feel of hopelessness and showing life that is nobody really would wish to live. Very often games that claims to be Cyberpunk are actually not, for example, Deus Ex: HR is a pseudo-cyberpunk sci-fi because it doesn't have that cyberpunk's gloomy desperation atmosphere. Here are the main concepts of such atmosphere:
1. Corporations rule the world, the governments are just puppets for real power holders. And corporations are not interested in people's well-being, only profits matter, their own employees are working in slave-like conditions, taking a lot of abuse from employers, barely keeping their ends together. Most work is automated therefore actual need for workers is small, which creates an insane competition for work places, which are taken by people who can afford better augmentations/implants, which they can buy only to become indebted for life, which in turn create a vicious circle guaranteeing that everybody is a looser except the select few. Loosing a job equals to death sentence because unemployment is so huge that a chance to find a new work is almost null. There is no small or medium business besides illegal/criminal business because corps doesn't allow for competition. This is really important to show right.
2. Hypocrisy is rampant: media propagates that the society has freedoms, opportunities are equal, everybody has a choice, and similar modern bullshit just exaggerated manifold. Hypocrisy is not blatantly obvious though, it's very subtle and most people are actually buying it. Thinking otherwise is considered being a traitor/unpatriotic and such people are marginalized and criminalized. Person's birth social status and wealth of parents decides if the person is able to have a decent life due to ability to buy enhancing implants/augmentations. Those people are usually ones with jobs but their life is shit anyway because they had to sell themselves practically into slavery for their augmentations. Most people though will tell you that it's how it should be because one needs to work hard to achieve what they have. Such people really don't have anything despite the illusion of a decent life because their debt to the augmentation companies means that if they're loosing job means they loose everything including remote deactivation of their augmentations, after which most people would commit suicide, sometimes even by the whole family.
3. Police is just another corporation that covertly serves those who pay them or corporations pay them not to meddle in their business.
4. People who cannot afford augmentations or implants are all lowlifes. There is absolutely no escape from this lifestyle unless resorting to crime. Most of them live on charity from corporations who sometimes use them as political tools, cannon fodder to mess with their competitors, use them as unwilling organ donors and similar purposes. They would kill each other literally for 5 credits or food, they are that desperate.
5. All people except select few are pretty much enslaved by corporations even if they are relatively high ranking within their corporation. The enslavement is not achieved by old style means of threat of use of force, cruelty, or death, it's a debt enslavement. For example, almost nobody can afford to buy augmentations but augmentations are absolutely necessary to get a job or even study in school successfully. The only way to get them is to take a loan from a bank or a corporation that produces those augmentations. To repay the debt you have to work all your life and give up most of your salary to cover debts or may be even more than your life, in which case you sign a donation of your body for organ harvesting at the age of maximum 50 or earlier. Another way of getting more debt are diseases: pharmaceutical corporations create new chronic non-lethal diseases and a drug to keep the person in working condition but not to cure completely then they spread them among the population and make sure people are paying for their drugs all their lives. Competitors actually interested in curing rival company's diseases but infect people with their own biological inventions.
6. Total surveillance if you're within corporate environment. Having a private uncontrolled life is a breach of contract and leads to the loss of job, which is in turn is almost as good as death... or worse. Most corporations put implants in their employees to record every their move and make obligatory life reviews once in a while.
7. One cannot really earn non-negligible money unless resorting to illegal activities or, may be, prostitution (it may or may not be a crime in the setting). There is just no other way even if your job is within wealthy corporation. If a person works
8. As Romans said: homo homini lupus est. There is no trust inside society, the society is cynically cruel to people, scamming and lies are a common place, survival of the fittest prevails. No one can change anything about that, no one can be saved, helped or rescued in the long run. Life expectancy is low, few people can afford retirement, most people die while still working, often committing suicide or selling themselves to organ harvesters to pay for their children's augmentations.
9. Outside of the corporate structures decadent life, drugs, prostitution, gambling, scamming, and petty crime is rampant. Mostly everything here is a grey economy powered by illegally obtained resources. Inside corporate structures life is miserable due to total control over employees who live lives that are pre-planned for them by the corporate rules and codes of conduct. Some corporations provide their employees with entertainment, which might be considered illegal or grey area. It serves several purposes: improve employees happiness, have a blackmail material against their employees to guarantee their loyalty and extend control over them.
The concept above should create really depressing setting if done right. I have several more ideas how to make the proper concept of cyberpunk but it would be to long to explain here. So the ideal cyberpunk game would be the one that sets the right depressing mood, where you will feel that your protagonist is completely nothing in that world. I can call it even survival horror with smiley happy faces. The game should pretty much force the protagonist to go against the rules. To achieve the goal and you have to become a monster yourself to defeat monsters, alternative will not be pleasant. There is no happy end whatever you choose.
For example, a "typical" cyberpunk quest should go like this: the protagonist's girlfriend got kidnapped by some criminals and protagonist has a choice to rescue his girlfriend or just give up and find a new one. So, let's say he decided to go for the rescue option. After some info gathering, protagonist learns that his girlfriend is kept at some place but the bad news is that criminals put an electric collar on her, which will fry her on just a button press or if she'll try to leave the area. To try to deactivate the collar successfully you must have a certain augmentation which some engineers have but it's very expensive and you have no money to really get it. So, your protagonist has a choice: try to rescue his girlfriend without an augmentation or get the augmentation in a shady way. If he tries to rescue his girlfriend without the augmentation then he won't be able to remove the collar and she dies one way or another. To get an augmentation the protagonist needs to get it from someone. He knows two people: one man and one woman engineers who have them. Both of those are rather common people, so there is no real reason for protagonist to have something against them, so no "it's a bad guy/gal" excuses. One way to get it is to kill one of them in a way that nobody notice it for some time, chop the augmentation out of them, sell their organs to illegal organ harvesters to get money for operation to insert the augmentation to yourself, sell their other augmentations on the black market for the same purpose (or, maybe, hack them and keep them for your own use, if by some reason you have enough money from previous illegal activity). You need to hack (to prevent remote shut down by the manufacturer) and install augmentation from illegal surgeon until engineer's disappearance is discovered. This is one way to get augmentation but there is an alternative but no less sinister way. You can try dating the woman engineer, set her up or scam her, collect evidence of the inappropriate corporate code behavior, send it to her employer. She'll get fired from the corporation she's working in. Then protagonist can persuade her to commit suicide. When she does that he chops the augmentations off and run to the closest hacker to deactivate remote shut down chip, alternatively bribes Police officer that come to investigate to share the profits from selling her augmentations on the black market, alternatively bribes him to ignore the case posing himself as a relative, alternatively sneak in and chop out the augmentation from morgue and mess with augmentation ids to be sent for deactivation to secure time to hack them. So, if the protagonist gets the augmentation he can free his girlfriend from criminals successfully. Prepare for fat lies though because she'll ask you where you get that. If you say honestly she'll later commit suicide unable to live with that burden.
As you can see, that quest is messed up no matter how you solve it and that's what I believe is the real cyberpunk atmosphere should be like. Pretty much by the end of the game the players should be seriously thinking about the meaning of life and what they're living for.