The footage showed a firearms officer striking a man twice as he was prone on the floor.
A police officer is now facing a criminal investigation and has been suspended from duties.
Protesters in both Rochdale and Manchester have claimed officers had used disproportionate force.
GMP said three officers were assaulted while they were trying to arrest a man following “reports of an altercation between members of the public in Terminal 2”.
They said the officers were “punched to the ground”, including a female officer who suffered a broken nose.
All three needed hospital treatment, the force said.
“As the attending officers were firearms officers, there was a clear risk during this assault of their firearms being taken from them,” a GMP representative said.
Four men, aged between 19 and 31, were arrested on suspicion of assault and affray and have since been bailed.
Speaking on Thursday, solicitor Akhmed Yakoob said Muhammad Fahir Amaaz was the man who had been kicked, and that his condition worsened a day after the attack.
He said a a scan revealed “a cyst on his brain”.
Mr Yakoob said he was representing both Mr Amaaz and his brother Amaad, who was also involved in the incident.
He added their wider family, who are from Rochdale, included a serving GMP officer and had been left “traumatised”.
