As a professional videogame programmer, I can assure you that I haven't heard functional programming discussed much at work or among other peers in the industry. Videogames are giant, data-intense state machines, with lots and lots of state to track and manage. My feeling is that it's really not a great fit for functional programming. Traditional object-oriented programming is *heavily* used (C++ is the defacto industry standard language), because that's a reasonable and proven way to encapsulate complex, independently-operating entities into well-behaved packages of data + code.
It's the same reason that the industry doesn't extensively use unit testing for engines and game code (not broadly at least), which may surprise some programmers in other fields. The reason is simple: many game engine tasks can't be boiled down into simple algorithmic data transformations that can be checked and verified by a simple function. For instance, how would one write a unit test to ensure audio is playing correctly, or a graphic shader is working as intended, or a physics engine "looks" correct in realtime interactions? It's not really practical. Thus, videogames tend to rely on integration tests using QA team members to spot anomalies.
In short, not every programming paradigm can be effectively applied to every problem. That's not to say you *couldn't* write a game purely in a functional language, of course. I just don't think you'd be working to FP strengths.