To make sure that you are playing this game in the right library, you must go to the Dota 2 library and select your library. Then, you must click on ‘Hide’ and then ‘OK’.
How do I permanently delete Dota 2?
Open your Library and right-click the game named Dota 2 Test. Select Set Categories. Tick/check Hide this game. Click OK. It is now hidden in your library.