I've not tried, but would be nice if AppGameKit would have actually ever tried to get it to work or if it doesn't work just say so...
You should also be able to tweet by url
https://dev.twitter.com/docs/intents#tweet-intent
On Android this will open the twitter app if it is installed. If not it will open the website and ask for a login if needed.
I wonder if it needs something added to the plist URL scheme like Facebook does? I can't find any information on it.
I find it funny that TGC doesn't have any apps with twitter in it that they can test this with. You'd think they'd have a full feature app that they can test out everything on...