The last game that really drew me in (OCD, had-to-finish, where-does-the-plot-go level I mean) was Portal 2. I really enjoyed the game but I also really wanted to see where the story was going. Bioshock Infinite was like that as well, right up till the very end when it turned into an eye-rolling cliche of an ending (IMHO it thought it was being a lot cleverer then it actually was). Tomb Raider (2012 edition, they basically re-released the same game twice over since then!) was one I also wanted to really play just to see what was going to happen.
I've played a lot of games that I've enjoyed, but they were the among the few that really drew me in from a plot point.
Try to Blade of Darkness with a headphone. The music is so awesome that it will (or it may) scare you. When I played it the first time (around 15 years back and was very young), I had to play without headphones (or any music: muted). And it is a freaking awesome action game.
When in doubt, go further back. In preparation for Cyberpunk, I recommend the following vintage titles for netrunners and solos alike.
Disks of Tron (arcade)
Tunnel Runner (Atari 2600)
Berzerk (arcade or 2600)
Syndicate (snes, genesis, or MS Dos)
Perfect Dark (n64)
Jet Set Radio (dreamcast)
Meanstreets (MS Dos)
Latest one to really blow my mind has to be Hellblade: Senua's Sacrifice. It's an incredibly beautiful deep dive into the psyche of a person suffering from psychosis. It might seem a bit short with it's 6-8 hours playtime but in the end I think it was just the right length. Really an unforgettable experience.
I just realized I haven't finished a game in a long time... well not all games have an ending but anyways: This list doesn't have any titles after like 2015.
Starcraft - It's free now and I can still remember huge chunks of the campaign it has a certain flair I think it holds up even after all this time. RTS
Half Life - I think it's free now, creepy, weird, a classic. Ego Shooter
Mass Effect 1+2+3 - I really enjoyed my time playing, good times. There are a lot of versions though with add on's but just the updated versions without extras are fine. RPG
KotOR 1 + 2 - great Star Wars games... if they just had fashioned the new movies after those games. I think there are only the vanilla version. RPG
The Last of Us - watch this video, get creeped out and start playing
Heavy Rain - Play Station exclusive but awesome game where your choices matter, your characters can die without the game ending, there is no game over, life continues one of the games with the most emotional impact I've played. RPG
Portal - a puzzle game like no other just very good - is there a genre for this?
The whole GTA series. Action Adventure
XCOM Enemy Unknown with the Long war mod. I loved it, still playing it from time to time, but it is hard. Turn based tactical
Fallout 3 - maybe the best RPG I've ever played. Incredible soundtrack, no add on's needed.
I just checked and except Heavy Rain and XCOM every game I mentioned is also onthis listand to be fair XCOM's predecessor is on the list.