Yes, your NFT will always be linked to object 238947872, but absolutely nothing about NFTs makes object 238947872 "a game sword" or even "a valid object in Game A", much less "Equivalent objects in form an function in both Game A and Game B".
Even if you somehow encode the visual representation and the stats into the NFT, using the most awesome method you could ever think of, that does not stop the power creep in a game.
Your Sword of Awesomeness does 3600 damage per second to the undead. You paid 36 ETH for this insta-kill weapon, and no undead could even be in the same instance with you without instantly becoming re-dead. Then the game gets a new zone where undead enemies have 40000 hitpoints and generate 7200 hitpoints per second. Your expensive sword is now a very impractical toothpick.
Even if you could make the stats permanent, you can't make it's usefulness permanent, nor can you guarantee it will be valid in any game for ever, much less several games at the same time.
Am I wrong? I want to know. Please elaborate on how you solve the "Object 238947872 is now a bag of chicken feed" problem and the "Object 238947872 is now obsolete because of power creep" problem.
Not even being sarcastic here. If I've misunderstood this whole thing, I want to know.