Quote: "Graphically many of them do, and there are many core gameplay mechanics that cannot be changed."
Well that's the thing. When you buy a game engine, you fit it with your own assets, and it can look completely different than other games if that's your wish. I don't understand how a game engine can be styled for a certain type of game i.e. WW2, gothic, etc. Those are assets that you can change. There's no way you'd want to use the stock assets
I have seen Quake mods that couldn't look more different from Quake, quite simply amazing transformations with the engine. If you didn't know it you would never guess it was made with the Quake 2 engine.