That's Buzkashi a sort of polo, really more akin to an American rodeo event than polo or soccer on horseback. But goats are as commonly used as are sheep, though those are not the only ones used for such sport, and more usually the entire carcass is used- the idea is to show the ability of the horseman [chapandaz] at grabbing up the critter at full gallop, as during a raid on an unsuspecting camp.
The Bedouin, in particular the Libyan Sunussi, enjoy something similar, though their game uses a rolling head, so something of the sort may not be entirely unknown in Iraq.