I can pretend I'm shooting monsters in my head too, but it's more enjoyable when playing Doom. Though admittedly this metaphor would probably have a sudden drop in happiness the closer to real it got.

Well, sure. But in one case you have a chance of winning (although vanishingly small), and in the other you don’t. So it’s much less entertaining.

You could find a winning lottery ticket, so without buying you do still have an (even smaller) chance. While one is sufficiently likely that it'll happen to someone and the other probably won't ever, neither will happen to you.

I think the bigger difference is probably the prop and the immediacy of the experience.

Yes.