This is a great question. I've been playing with pure functional programming, and I also noticed that applying it to video games is very hard. In other areas, FP provides many advantages such as testability and safe parallel execution. But for simple games these are not that useful. Simple games seem very well suited for the imperative, global state model.
There is one aspect that might make FP worth it for games and it's interactive programming. The immediate feedback loop described by Bret Victor [1], with the possibility of going back and forth in time is easier to achieve with a pure functional approach.
The Elm debugger [2] is an implementation of this concept, using hot swapping and functional reactive programming it's possible to design games interactively in a very unique way that it's hardly achieved with the traditional imperative approach.
[1] https://www.youtube.com/watch?v=PUv66718DII [2] http://debug.elm-lang.org/