> refers to the game of Nardshir, as is a good mind stimulant. Rashi explains this as Chess.
Nardshir from Persian Narde, is backgammon and indeed a reference to Ardshir king. So, Rashi got the history right, but not the right game. Wiki brings this Gemroah as the first historical reference to the game. I thikn chess and backgammon are different enough to be confused or exchange names.
Ardshir is a Persian version of Xerxes, so maybe a hidden reference to Ahsahverosh?!