Stock is certainly a security. Stock options are just call options of a security, and also a security. Obviously there is some (future, conditional) value implied since it's a reward.
It doesn't really matter whether you are trading stock for dollars, or work, or fb likes, or whatever--it's still a general solicitation because they are being traded for something.
Caveat: I'm not a lawyer but I have been involved in startups in the space for many years.
There is precedent of an almost identical enforcement action by the SEC, but my google fu is failing me.
But, I would think a line of defense would be that participants knew they wouldn't necessarily get anything for participating and presumably agreed to that in contest terms. At that point, the contest is just a giveaway -- and you can, in fact, give away stock.
The surprising part is that Jet.com's legal department let this fly.