Wow, so she invited people who most likely could not or would not attend, and also told them she essentially couldn't be bothered looking up their address or even requesting it?
"What are your thoughts about this FB invitation? What are the expectations/obligations of the invitees? "
1. Gift Grab (seriously first thing that came to mind).
2. You have no obligation here.
What I would say is that if you were planning to or would normally send this particular child a card or gift then please proceed with it, a 6 year old should not miss out because of her parents manners.
If you were not planning to send anything anyway, then a simple rsvp no plus a happy birthday post on FB seem perfectly appropriate.