maybe some flashy casino type games that give a dopamine hit, edit: oh you mean like a real gamer.. maybe some pro golf games
He'd play a heavily modded Elder Scrolls game where it's just people saying "sir, sir" and calling him the best at everything right from the start. 
I found a YouTube link in your comment. Here are links to the same video on alternative frontends that protect your privacy:
what game allows his success to be carried by his parents wealth and his sycophants obsequity
Oof. So fucking true. Entire patches of the game were put in place just to protect the country clubbers that the devs established.
From his general mental faculties and his extensive history of assorted sex shit, I'm going to say that if Donald Trump were a gamer, that he would probably spend most of his time on Bubble Shooter and erotic visual novels.
LoL, his first impulse to start shitting on everyone else in the match would fit right in. He would only play AP Teemo and wander around planting mushrooms. "We love trolling junglers trying to get a kill don't we folks?"
In my mind-palace Trump is a Sega gamer obsessed with Sonic and Shenmue, but in reality it'd be something chudy and boring like Fallout 4 where he's evil in every playthrough.
but in reality it'd be something chudy and boring like Fallout 4 where he's evil in every playthrough.
I think he'd be more like a Fallout 2 metagamer that racks up karma in ways that makes him feel heroic while doing the most evil shit possible between karma farms so he can also feel like the hero.