That's what the escape hatches are for. In Coq, for instance, you can also write functions processing infinite streams, provided that they also produce something regularly. For example, in a game, you could write a function from an infinite stream of inputs to an infinite stream of frame updates. You can not write functions that would not terminate while computing the updates for some given frame.

Alternatively, you just write a function to iterate your game world update N times, where you choose N large enough to ensure that your game can run until the heat death of the universe. That's not a nonterminating function, but it's long-running enough for all practical purposes.