Find out directly what GCW has to say, once you lay out your cards on table.
PS Watch your back. I hate to say this, but I wonder if one of your CW's is some sort of a mean girl who has engineered this whole situation for her personal amusement.
These are good points, and part of why I wanted clarification on where the "you will bring a present" thing came from and if it was told to GCW if it didn't originate with her.
On one hand, it might very well be that GCW is caught up in this culture and playing an active part, not really wanting you at the party but still wanting a gift. In that case, I think that the hard line advocated by some of the previous posters is absolutely the way to go.
But on the other hand, it could be that GCW has no idea what's going on, that all this is going on around her with her as much of a prop for amusement as the OP. Somehow they convinced her that OP doesn't like parties, to the extent that extending an invitation to her would upset her...but that also, OP has positive feelings and still wants to give her a gift. (And why shouldn't OP have positive feelings? She's never had any clashes or disagreements with GCW.)
I'm imagining myself in GCW's position if the second scenario is the case. The most inexperienced person there, being suckered into thinking certain things about a co-worker, acting in genuine good faith by not inviting co-worker to a party, being told that she still really wanted to give me a gift, and then....it all blows up in my face because co-worker is obviously really mad and doesn't give me a gift after all. Not because the gift itself is important...but because I've obviously offended her in some way even though I was acting in good faith.
Now, OP is still not obligated to give a gift or do anything for the party. Especially not do anything for the party. But I think that OP should ask herself: If she had been invited to the party, would she have gone? If she had gone, would she have brought a gift?
I think that if everything had not been so weird, and she was either invited to the party and would have given a gift or would have given a gift if there had been no party and others were just giving her gifts, I think I would go ahead and give the gift, maybe a token gift or just a card if the OP didn't really know her all that well, in private at some other point. This way, GCW isn't penalized for the actions of the other co-workers if they have truly suckered her in and are setting her, and/or OP, up for a fall.
But if OP does talk to GCW beforehand as suggested, which I think is also a good idea, OP can get a read on which of the two scenarios is most likely and act accordingly. I'm just asking that OP be open to both potential scenarios, and if GCW is another innocent party, try to find a way to honor her without helping the obnoxious co-workers, who would be the ones at fault if that were the case.