Do the players levels serve any purpose/are they intended to serve a purpose?
Aside from satisfying you for beating out even me? ;-)
Yes, I intend to have some games restricted to players of some minimum level. I know that in all such games, experienced players sometimes want to play only with other experienced players, to have a real shot at beating the game. So there will be games where you have to be level 1 or level 3 or something to join.