It's not so much the tape that would help Irvin but having the time to strategize and mount a PR offensive. With no tape out there, the only thing public is Mike outing himself as not remembering due to drinking. So yeah, you desperately want the tape so you can figure out what your next move will be. If it's damning, then how do you slink away looking as clean as you can? If not, then how do you spin this to rile people up to rally behind Mike to lift his PR rating (the whole point of this lawsuit) while making those of Marriott/NFLN/ESPN look worse? The latter is what Irvin's lawyer is trying to channel with this "We're incredulous!" spiel when, as the article also points out, the video WILL be provided once a court order is given.
The thing lost here is that what Irvin said in his radio interview was that Marriott claimed he "said" something to an employee. Not sure how video is going to prove what he said unless there's audio, which I think is unlikely unless Marriott's got some audio thingy in their lobbies. So if there's just audio with no sound and Mike's claim is that he was accused of saying something, what does that prove? There's nothing for Marriott to pay in that case. So then it just leaves Irvin's team to to make their PR pitch that Irvin didn't do anything even with no audio to prove he didn't actually do anything. Marriott is a corporation that can refuse service if they want to, and even then they didn't refuse, they just moved him.
And regarding the witnesses, this is the point I continue to make: the witnesses only back up that there was no physical altercation. According to Mike himself, this isn't about physical, only audio. The witnesses didn't hear the audio of their interaction. So all the witnesses do is confirm for those who again think that a person offended/threatened by a comment has to react right then and there in the moment and that's not the case a good number of times, especially when you throw in the power dynamic at play.