KABUL, Afghanistan — As heavy snow fell on the muddy arena in northern Afghanistan where a traditional game of buzkashi — two teams of horsemen fighting for a dead goat — was underway on Friday, a scuffle broke out near the stands.

It was not just another group of hotheaded fans going at it. The man who had thrown the punch is the vice president of Afghanistan, Gen. Abdul Rashid Dostum. And he did not stop there: To drive the humiliation home, he put his foot on the chest of his downed victim, a political rival named Ahmad Ishchi, who was then beaten by the general’s bodyguards, thrown into the back of an armored vehicle and taken away, said several of Mr. Ishchi’s relatives, many of them speaking on the condition of anonymity out of fear of retaliation.

“Dostum came there, and he walked around the stadium, — then he called Ahmad Ishchi over to him,” said Gulab Khan, a relative of Mr. Ishchi who was among about 5,000 spectators at the game. “After talking with him for a couple of minutes, he punched him, and his bodyguards started beating him with AK-47s. They beat Ahmad very badly and in a barbaric way.”

The account of General Dostum’s actions — while not unexpected for a former warlord with a history of accusations of human rights violations and abuse, including physical acts of retaliation against allies and rivals — underscores fears about someone a heartbeat from the presidency.