Before you start messing with permissions, could you run this to check if it is really related to permissions? This will run Dolphin as root (obviously a bad idea but fine if you're just testing):
gksudo /usr/games/dolphin-emu
Dolphin's binary is in /usr/games, which is not in root's PATH. This is probably what caused gksudo to fail if you simply used "gksudo dolphin-emu".
gksudo /usr/games/dolphin-emu
Dolphin's binary is in /usr/games, which is not in root's PATH. This is probably what caused gksudo to fail if you simply used "gksudo dolphin-emu".
