An Entity Component System is literally the functional approach to programming under a different name and with mutation by default. There’s even been a huge move toward keeping ECS data classes separate from behaviors. At that point, it’s just a less ergonomic functional approach with better performance due to lower-level languages (though ATS or Rust are just as fast as C).

Maybe you’re thinking of FRP (functional reactive programming), but that isn’t even super mainstream among most functional programmers. I know some small games have used it, but it’s mostly used for specific kinds of UI in languages that enforce immutability and no side effects.