That's the preferred protocol for ultra-real-time games because a few ms ago is not helpful information to spend time recovering. A sufficiently fast-moving MMO could apply
Anything with real time communications like an FPS would use UDP as stale action data is mostly useless. The latest state of is all that matters.
Most such games will either layer their own streaming channel atop UDP for guaranteed ordered delivery of important messages or use a separate TCP socket as well.
You must not be looking very hard, pretty much every game engine uses UDP as the network transport. There are some notable exceptions like Java Minecraft.