- There were 108 suitors (we know this from the Odyssey 16.245-254 [1]).

- All that Homer told us is: They were gladdening their hearts at pessoi in front of the doors, sitting on the hides of oxen which they themselves had slain (the Odyssey 1.106-108 [2]).

- You can't have 108 sitting men play the same game of marbles.

IMHO, pessoi was a 1:1 game and it was not a board game.

[1] https://www.perseus.tufts.edu/hopper/text?doc=Hom.+Od.+16.24...

[2] https://www.perseus.tufts.edu/hopper/text?doc=Hom.+Od.+1.106...

Like you wouldn't call (Kievan) Rus' "ancient Russia"