vague game idea that might be fun or might be too much of a pain...
Imagine playing something like The Little Mermaid (not Disney's version) - you're stranded in a new world, you can't speak to anyone, you have enemies trying to discredit you, and you're trying to accomplish some task, whether it be romance or something else.
As an adventure game, you can go around picking up objects, combining them, and showing them to people. You can also communicate in sign, except of course that you don't know sign at first and you have to pick up new symbols as the game progresses by interacting with other people, who will eventually show you ways to refer to different things.
So at first pretty much all you can manage is 'yes' or 'no' but slowly you develop a more complex vocabulary.
Could even use real sign language for an educational bonus, if you had sufficiently good animation.