Since the games pre-dated the Spanish, what should we suppose the Mayans were riding?
Where did you get that the men were mounted? All the Mayan murals, carvings and clay figures, as well as every account I've ever seen, indicate it was played on foot.
"Always wondered why the conquered Mayans of Mexico, Belize and Guatemala constructed the amphitheaters for games in which two mounted men would angle for putting a stone through an embedded ring approximated 8 metres high on one side of the arena, each being permitted to attack the other, all for the pleasure of royalty. First stone through was the winner...."
Those balls weren't stone, they were raw rubber.
The game was a religious ritual, deeply entwined with Maya Cosmology. Scoring was extremely rare, and when a team scored, it won...and was sacrificed!
As I understand it, the game was a ritual pre-enactment of the passage of souls into the "Tree of Life" at the center of the Galaxy, which is supposed to take place at the end of the 13th Baktun of the Mayan Calendar (December 21st, 2012 in our calendrical system). That date was extrememly significant to the Mayans.
Here's some good background information on the significance of that date:
http://www.levity.com/eschaton/Why2012.html