This is the way. Each non-Steam game you add is basically running in its own box, so the trick is to add the installer as a “non-Steam game”, enable Steam Play compatibility as artiman said, then “play” the installer. Once that’s finished, go into the properties of the “game” you added, and change the path to the now-installed game’s exe. It’ll be in a hidden folder, so you’ll need to enable “show hidden folders”, and find it under something like Home > .steam > steamapps > compatdata > (a very large number) > pfx > drive C > wherever you installed it. Don’t just add the exe as a separate non-Steam game.
This is the way. Each non-Steam game you add is basically running in its own box, so the trick is to add the installer as a “non-Steam game”, enable Steam Play compatibility as artiman said, then “play” the installer. Once that’s finished, go into the properties of the “game” you added, and change the path to the now-installed game’s exe. It’ll be in a hidden folder, so you’ll need to enable “show hidden folders”, and find it under something like Home > .steam > steamapps > compatdata > (a very large number) > pfx > drive C > wherever you installed it. Don’t just add the exe as a separate non-Steam game.