I think you're looking at the left wing (number 1) engine; GP is talking about either the tail or right wing engine. (I think tail is number 2 on MD-11.) There's a brief explosion visible through the smoke at about 1-2 seconds in, to the right of the engine visibly on fire; that's probably what he's talking about.
Freeze frame: https://imgur.com/a/c3h8Qd3
Yup makes sense. Now seeing photos of the entire left engine on the ground by the runway and the implication that however it failed it might have damaged the tail engine.
Agree, looks like an engine disruption.
The rotation already exacerbates the flow into that engine. Change in flow geometry gets more smoke in its way when it's already eating turbulent air.
We don't know if it just had a disruption or a full-blown stall, but give the way it made it to takeoff speed and then just gave out, stall seems likely.
And having 2 out of 3 engines fail (or underperform) would explain the insufficient climb thrust.