I don't see why it wouldn't. You're probably thinking of just Candy Crush and company but I have games like Final Fantasy 7 and Baldur's Gate on the iPhone. Though more interesting from a money standpoint would be major online games like Fortnite and League of Legends on the iPhone.
Every time I want to play a game I have to consider if I want to bust out my laptop, turn on my TV system, or just swipe over to a game on the phone I'm already holding.