It's not a virus, it's just a thing that invites all your friends.
What's the difference? It's a web virus of sorts, isn't it?
You could argue about the precise definition of a virus and all that, but I think this classifies more as malware that just spreads around. Spam-ware maybe?
A virus needs to be 1) stealth, 2) have a malicious payload, and 3) be self-replicating.
That was my thought - Facebook Spam, not a virus.
BUT that's a side point to an annoying trick that's been well-spotted, explored and explained by the OP.