I didn't see the "claim steam key" section on some of the game's (which provide steam keys) download pages
I saw this too. I suppose not all games support it? Perhaps check the game's FAQ for mention of Steam - they might have chosen not to be on Steam.
I have this same problem! Because I created an itch.io account and didn't originally link it to my steam account it looks like i don't have the option anymore. I can only download it directly from here
