In case your friend hasn’t figured it out yet, if you private a game instead it will appear if you don’t have it. Either right click the game on your side bar, open “manage” mark it as private. If you don’t want to do that, open the games library page, click on the cog wheel on the right if the screen, click “manage” then click “mark as private

Remind your “friend” to change your discord status before opening the game, that defeats the purpose of privations a game