Personally, I'd complain to the game creator. Even games shouldn't be allowed to get away with the lack of a keyboard interface.... (well, except console games for obvious reasons).
It doesn't immediately solve your problem but if enough people want it they may have "no choice" but to add a working keyboard interface.
In fact, they very well already have one. If you are able to navigate your "inventory" (if that is what it is) using the arrow keys, you might also be able to use the Application key to show the menu. I don't know, though-I think the menu shown would probably be the same menu you get from right-clicking the applet.
Also, this might sound crazy, but you could try an entirely different keyboard. the keyboard you are using could have something wrong with it or the bounce detection IC could have failed (so when you release the key from a "firm" press it registers a second "bounce" press. This would also ignore the keyboard repeat rate and delay settings since to the computer it appears as an entirely separate keypress. I'm more totally guessing, but it is feasible. And if you have an extra keyboard lying around it's free to try.