I think they just don't keep the contact list. It is uploaded, but only matched against the list of subscribed users at the time of the upload and then deleted. Only downside is that if a contact joins later and does not have you in its contact list you don't get notified, or only when you recheck your contact list.

Your link above says at the end:

For TextSecure, however, we've grown beyond the size where that remains practical, so the only thing we can do is write the server such that it --- doesn't store the transmitted contact information ---, inform the user, and give them the choice of opting out.