So..........I bought Sim City 4 here on GOG, and..........the play button went gray. Help?

Sometimes when a game launches it can fail so there may be processes of the game still running so Galaxy thinks you're playing the game. Try looking for these processes and ending them and try to start it again? If this keeps happening I'd reccomend a reinstall.

how do you run it outside of galaxy. it's not loaded directly on my desktop

If you don't have a shortcut on the desktop, just go to the game's directory.