it's up to the nft originator to assign ownership in just one jurisdiction. if they create and sell multiple nfts in different venues, but for the same item, then i imagine that would damage their reputation and the value of their prior and future items. the chain itself does not assign ownership independent of the nft originator. with art i think nfts do function very much like certificates of provenance. game items are different in that the community of players, or the company hosting/developing, indicates the proper database source (chain).