I will help clear up some confusion if I'm able.
First, I don't think the big use case is for items being traded between different games. However, a system like that is possible. Blizzard would be a good example here, since their games have a high degree of cross-pollination, and they frequently offer promotions that unlock similar items in several of their games at once. So, owning a Blizzard "magic sword" token might give you a sword item in WoW, another one in Diablo, and a sword card in Hearthstone, each adapted for its own game. This is a small use case, in my opinion.
I imagine that the big use case is for any game developer (indies especially) to leverage the marketplace without having to build one, or be locked into one provided by a single publisher/distributor. The game itself does not have to be p2p as you're suggesting. Game architecture would remain centralized, and would communicate with a blockchain where the tokens are stored.
The process might look like this:
1) A player purchases an NFT representing an in-game item issued by a wallet owned by the game developer.
2) The player sends that token to a smart-contract address, also owned by the developer, with a memo that identifies their player account.
3) The smart contract notifies a centralized game server, then sends the token back to the player's wallet.
4) The in-game item appears in the player's inventory, within the game.
There could be any number of steps involved, and the contracts could operate however you'd like. The token could be destroyed after a single use (like purchasing keys for loot crates in CS:GO) or used and traded any number of times. The game server would have to keep track of which player account controlled which token, and update players' inventories whenever the token changed hands.
One more thing - NFTs can be programmed such that creators receive an automatic royalty (a percentage of the sale lands in the creator's wallet address) whenever the item is sold on the blockchain, no matter who is selling to whom. This could be huge for indie developers, who would benefit not only from selling the original items up front, but also from the long-tail resale of such items between their players.