The male passenger and the male AA employee in the blue shirt (probably a flight attendant) were both clearly way out of line from the video. An AA customer service employee saying "you wanna go?" and inviting a fist fight, as he did, is beyond the pale. I'm glad to see that AA has suspended him from duty while it investigates. The male passenger's behavior was also clearly unacceptable, but that doesn't excuse the AA employee's reaction.

And by the time the video started, the AA employee had hid his name by putting his badge in his shirt pocket.

We can't tell who was at fault for the initial incident, but the blue-shirted flight attendant's behavior in the video makes it easy for me to believe that he did violently grab the stroller as passengers claimed. This makes it sound to me like it was an unusually small stroller that really would have fit in the overhead bin as a legal carry on; if that's true, an AA employee asking the passenger to gate check a stroller reflexively is understandable even if incorrect. But that doesn't excuse grabbing the stroller in such a careless way as to almost hit a baby with it.