It sounds as if you have installed the ROMs with root permissions only – you need to change the owner and the group of the ROMs directory (and, to make it easy, the rest of the RetroPie directories as well) to “pi”. You can do this with the commands
sudo chown -R pi /home/pi/RetroPie/ and
sudo chgrp -R pi /home/pi/RetroPie/
Reply To: When I select game it won't play and says permission denied?