Lightspeed -
There are options that can change that. The program automatically checks the clipboard for spelling, some programs use the clipboard in weird ways. You can disable this. Also there is a list that you can add a program to and it won't check that program for spelling. That should solve that stuff with the game...ect.
To others:
It is indepedent of any other program, so you can run it with whatever program/plugin you want. However, I would only use this and not the spell check plugin....but that's just me.
Also, it doesn't check a word until you are done typing it with either a space at the end or return...ect.
So, if it is the last word of the sentence and you hit return to input it into Hal, it will check the last word when you hit return. I haven't looked to see if there is an option to change this, so I'm just quickly adding a space then backspace at the end of the sentence to have it check the last word.