I have No Time To Explain Remastered and the delisted original version No Time To Explain in my library. The original is delisted from Steam Store, but I can still download and install it. Would this game count to the amount of perfected games for my profile?
I completed the original version of Skyrim on Steam after it was delisted. The Perfect Games count went up by one.
Update: Found a way to prove it :).
This post makes clear Skyrim was already delisted at 16th March 2018. I got my last achievement on 25th of May 2019.
Here is the proof that it counts as Perfect Game
I have 100% in Dark Souls: Prepare to Die edition, which is no longer available to purchase because of Remastered version.
However, it's still counted as one of my perfect games:
If a game was published with achievements on Steam, the tracking of those achievements will keep working regardless of the status of the game in the store: either delisted, superseded, or similar (I'd dare to say that this is true even if the publisher gets banned). As long as the game is in your library and had defined achievements at time of purchase/redemption/activation, it will work. Same for the community hub for the title. A game may not exist in the storefront anymore, but the elements of the community hub will keep being available unless there is a violation of the community guidelines (and consequent admonishing) by the developers/maintainers of the game.