I had the brilliant idea of adding Excel and PowerPoint to my library as non-steam games (yup...). At some point, I wanted to remove them. However, surprise, surprise, the "Right Click / Manage / Remove non-Steam game from your library" option was gone. In fact, the only option I got from Right Click was "Launch", "Add to Category" and "Properties".
So I spent a couple of minutes looking around and the best solution I was able to find was a way to remove all non-steam games from the library. This didn't work for me, since I only wanted to remove those two and keep the rest.