League of Legends has been only determined as playable when using Intel® HD Graphics video controllers. Still the error message that you have showed does not clearly indicate what may be the root cause of this issue.
From our side, we suggest that you have the latest drivers and BIOS for that system, update the Microsoft* .Net Framework and latest Service packs for the operating system, as mentioned on the system requirements for the game on the game developer's web site and then check with your game developer for any update for the game.
Furthermore, you may check with the game developer and debug the root cause of the issue and check if the system meets the requirements to play that game.
