My own definition of an engine is a card that generates points passively, without you having to interact with it after you play it in order for it to gain value. I don't think there is an engine card in this game that generates value without a condition. Or I can't think of them now.
I really wanted to stay away from this discussion, the whole BFG vs selfeater, spender vs engine, as it will lead nowhere, it's just two sides of people each with their own definition, and one isnt necessarily better than the other.
But what you said in this quote, its not what's generally agreed in the community:
There are active engines and passive engines.
An active engine is when you need to click it to gain value, for example a reinforced ballista.
A passive engine, gains value each turn without clicking, so even if you pass. Example: Kerack city guard.
Then there's another engine classification: offensive/ control or defensive/ boosts/ pointslam.
To use the same examples as before, reinforced ballista is an offensive engine, kerack city guard is a defensive one.