Yeah, this whole auction is oddly structured. If there's not a single closing time for all of this, then every closing time really ought to be on the thumbnail, not just in the listing. It also seems likely that the organizer of the auction is not necessarily a game show person, and therefore didn't realize that game used props are highly collectible in a way that standard swag maybe is not.
Also, what am I not understanding about the shipping rules? They won't ship it to you if you live in town, but they will if you don't? If they're charging for shipping (which they are), what difference does it make how far it's going?