EDIT: I also wanted to add in that the smart contract that supports an NFT can be made in a way that allows the original developers to collect fees on every transfer of the asset. This means it might even be in my best interest as the original developer to endorse other games using my in-game NFTs because the longer I can get people transacting with my asset, the longer I can keep collecting revenue. I might even pay other game developers to integrate my item into their game to make this happen.
So the likelihood of an item living on in another game could be quite tenuous. Not least because you have to hope the game developer supports your items and there isn't a strong incentive to do that.
The other side of it is whether these will have any meaning beyond being a nice reminder. In that sense you don't really need a token but to own your own data about the game. In this sense we can already see people holding onto the meaning of their previous gaming adventures, through maintaining friendships, keeping screenshots, diaries and other media about them and so on.