Endless titles showing as owned

Just looked it up and it indeed claims the games are already in my steam library on the storefront (but not in my actual library). However, if I click "Play Now" the startup dialog box appears briefly, vanishes, and nothing else happens. The game does not play, install, or add a license to the account.

However, that does at least say that the problem isn't steamgifts, it's steam. So if it remains a mystery, I'll probably give it a couple days to see if it's resolved internally before contacting support.