How to join a game as observer in StarCraft 2?
This isn't possible unless you started the game as an observer.
When in the game lobby screen, the host can right click on a user, and say "make referee", they then become an observer for the game.
Any participants who join into the game lobby after it's full will automatically be observers / referees.
This procedure can also be used from a game save, if the participants are willing to go back out to the lobby to make this possible.