No, I don't think "timeshare" is the same. In a timeshare, there's no exchange of funds between you and the people with whom you're sharing; you and your co-sharers are collectively purchasing a thing from a third party and sharing it (in this case, a rental property). It's like if I said I was "sharing a cab": you would assume I meant some other person or people and I all got in a cab and split the fare. The other passengers and I would be the ones doing the sharing, with each other. The driver is not sharing with us, and I would never use the word "share" to describe taking a cab alone.
Isn't that exactly how the word has always been used? For example, in timeshare which, while not a flattering comparison, definitely predates Airbnb.
EDIT: Oh, I see a similar comment has been stomped into the ground for some reason already.