Not any more so than car titles are fungible. If I give you $10k cash and you give me $10k cash we end up in exactly the same material position, despite owning technically different objects (dollar bills) than before. That's because the dollar bills are fungible tokens representing a value. But if we trade titles for cars worth $10k each, we are both now in a different material position since we own different cars now.

(The problem with NFTs in this analogy is that transferring car titles has legal weight, while selling an NFT probably doesn't without additional contractual language.)

They aren't. You're trading one non-fungible thing for a different non-fungible thing.

Alternatively, a game could also offer SFTs (semi-fungible tokens, as described in ERC-1155 [1]), in which case players could trade multiple identical versions of some indivisible asset. Something like a skin or a hat would be an SFT unless only one copy of it existed (i.e. only one player could ever use that skin or hat at any time).

[1] https://eips.ethereum.org/EIPS/eip-1155

They would be unique items that are identifiable from other items. (e.g. different hashes, even if they represent the same item in game) “There are many like it, but this one is mine.”

fungible = mutually interchangeable

NFTs = typically (and at a low level arguably always) non mutually interchangeable, aka unique.