When I go to play.google.com I see the listing for My Android Apps, this is not my Chromebook app listing. For the Chromebook app listing you need to bring up Apps (lower left corner) to see everything installed, and use the Store to select new apps that are compatible with the Chromebook.
FYI - to pin or remove apps, hold down the alt key with a touchpad click to bring up the menu
FYI - to pin or remove apps, hold down the alt key with a touchpad click to bring up the menu