I have a laundry list of games I'd like to see him play, many which he will never play for one reason or another, but at the top of my list of likely candidates:
Ready or Not
A tactical/police sim first-person shooter. The game sees you taking the role of a SWAT operator dealing with barricaded suspect and active shooter situations. The games tasks you with being able to make plans and execute them quickly and effectively with minimal loss of life, as you are expected to act within Use of Force protocols when dealing with suspects. You also need to be able quickly identify hostages and suspects, and make quick and accurate shots if things go sideways and a bad guy grabs a woman by the neck and starts using her as a human shield. Weapon modeling and handling leans heavily towards realism, so gun knowledge is helpful when making plans, but not necessarily required.
Given how he typically plays games like Call of Duty, I'd love to him go full-auto on his MK-18 and blow a civilian to kingdom come because he failed a PID check, or waltz on through the fatal funnel and get peppered from every direction because he didn't pie the door first.
Buckshot Roulette
We all know how much Phil loves gambling, and plenty of people in this thread suggested him to play Russian Roulette. Well Phil's never gonna buy a gun to shoot himself with, so here's the next best thing. Key skills include memory, probability crunching, and planning ahead incase things don't go your way, all of which are things Phil lacks. I can imagine how chat would try to fuck with him via backseating by feeding him false information, which would no-doubt be hilarious.
I eagerly await the day he plays this game in the next five years, and then wonders why no-one showed up to support his streams, because if there's one thing that's consistent with Phil, it's striking when the iron has gone completely frigid.