Yes it's official. It was on the 'Thank God It's Christmas' 12" single. I actually think the one on the 'The Works' album, was edited from that. I haven't heard it for a while, but I think that's what it was.
But that's why you should BUY the singles, you find nice treats on there.
While The Works did give us some great extended versions ( Ga Ga, IWTBF) I think that the extended version of MOTP is a bit repetitive and takes away from the flow of the song. (also just for the record it's the intro and mid sections that are extended, I think the ending is actually shorter)
it is one of my favourites from The Works, Fred Mandel sets the keys on fire.