It took work by a large parent company. And I don't know how third-party websites can trade those, but it must mean either Valve is managing an API or people are doing something hacky to work around that.
It's what I said above, it's a lot of work for a new game to create/maintain its own collectibles marketplace that people can trust, and even a well-established game like Counterstrike doesn't properly support third-party trades. Ethereum provides all that out of the box with NFTs.
There's also the issue that Valve controls all the assets, but that's mostly a moot point because they control the game anyway. I guess someone could honor NFT skins in a separate game if they really wanted, but that's getting theoretical.
They can't. There are third party websites but there is no way for them to initiate trades. They work around this bysome crazy peer-to-peer trust-me-bro scheme.