Seems like we are not watching the same video. The woman enters the video from the lower left corner as Irvin and the guy with the white hat are coming in the hotel doors. She turns and enters the bar and is hidden behind some kind of pillar as the guy with the white hat is just entering the bar with Irvin about 5 ft behind him. Since Irvin came into the hotel with the guy in the white hat, Irvin could be following the guy with the white hat as he turns towards the bar. You are assuming Irvin started the conversation because you see him turn towards the entrance to the bar area. But that is not on the video. You cannot see the woman as Irvin turns into the bar. When she steps out to the right she and Irvin are already conversing. You cannot see who initiates the conversation.
Besides, it is not relevant. Even if Irvin walked up to her and started the conversation it's not a crime, or offensive. If every guys who started a conversation with a woman in a bar lost his job an awful lot of men would be unemployed right now. Her words in her accusation matter.
And sorry, the burden of proof in this country is always on the accuser. In this case Irvin has filed a suit claiming she defamed him be telling his employer he assaulted her. If this video is supposed to back up her claim then she has a loser case. If Irvin did not assault her that would be defamation, and he suffered damages because he was taken off the air for Super Bowl week. The video does not show an assault of any kind. The question still remains, why did ESPN take Irvin off the air? If it was because the woman and the hotel claimed he assaulted her then Irvin has a good case for defamation based on this video.