Do the DirecTV HD Receivers have an optical output jack?

Yes

Is it the one to the left of the HDMI jack? If so, why does it look like there is a blue thing jammed inside of it?

Every optical input/output I've seen has had some kind of plastic protection. Either, in this case, something that swings out of the way when you insert the cord in or a plug that you need to remove. I would assume to protect it from dust?