If they really did this on the Wii, I might actually start a Twitter page.
There are some companies thinking about doing this for real. Make a major achievement in a game, and it will be automatically uploaded to your Twitter page. Same thing for MMORPGs. If your guild or friends go on a quest and do well, you could have the game auto-tweet so other people would know what was happening.
Of course it could also be abused and incredibly annoying. This was shown to the company who turned it off. Wise move...sort of. They just needed to tweak it to have it make sense. Don't do a "completed Chapter one" tweet. Instead, do major things. "Got a platinum trophy," or, "scored [x] points." How is that different from reading about your friends' bejeweled status on Facebook?
Twitter could be used wisely... if the companies think it through.