In this case it is obvious that this guy was refusing to leave, at that point he became a tresspasser. The officer then called for back up, and when all of the officers asked him to leave and he refused, then the police then called the idiot's hand.
They could have beat him into submission, but then they'd get sued. They could have sprayed him with mace, but then that would have endangered everyone else who was standing around cheering this idiot on, or they could have tazed him a few times.
As far as I know it isn't a crime to forget your ID.
Refusing to obey the orders of a police officer, tresspassing, disturbing the peace and resisting arrest are crimes.