You can go to the SteamDB page for a game, click App Info on the left, then look for the “Detected Technologies”. This will usually tell you what they’re using if it’s not a custom engine. You can use the Augmented Steam or SteamDB browser extensions to get a direct link to the SteamDB page from a game’s store page.
Also, SteamDB has a page here with aggregate data of how much each detected engine is used across Steam. Unity currently accounts for over half of the games using known engines (snapshot).
Edit: For non-Steam games you could check out IGDB.com. It has crowd-sourced data on all video games, including which game engine was used.