1.
There is a difference between assault and battery.
Battery involves touching that causes harm or offense.
Assault is causing the victim to fear a touching.

2.
The drunk established himself as someone likely to commit battery.
The drunk committed battery against the woman by touching her in a way that was likely to offend.

3.
The police were aware of the drunk's likelihood to commit battery.
To prevent future acts of battery they attempted to remove him from the casino.

4.
The drunk then committed assault against the police officer.
The assault was causing the officer to fear a touching by the drunk raising his hand to the officer's face. The fear was especially justified because the person has just committed battery.

5.
The police force was justified.
A bystanding officer is justified in using non-deadly force when he sees a citizen or another officer being assaulted. An officer is justified in using non-deadly force to end an assault against him.
The drunk was committing assault against the officer and the officer was justified in using non-deadly force to protect himself.

6.
The intentional falsification of police documents by police should be addressed.
The falsification however is a separate issue from determining whether the police used unjustifiable force against the drunk.