I mean I am not sure I'd go as far as to say Klopp bottled it, but he looks slightly deranged in that clip to me. I didn't see before or after.
Trying to be objective I would say;
1) Klopp says something to Dyche on the way past, which he ignores. Klopp then follows him havign a go.
2) Dyche says something back and stops.
3) Klopp then walks after him angrily gesticulating. Pauses when Dyche stops.
4) Dyche walks into the dressing room, and Klopp continues his tirade.
I didn't watch the first half at all, so not sure if anything prompted this, but looks to me like he's lost the plot. Did Dyche do anything in the 1st half to wind him up?
I'm sure Dyche would have loved to have got aggressive with him, but he looks in control of his emotions, and focussed on his job, which is to sort out a half time team talk. Klopp looks likes gone there. I've seen Moyes and Ferguson ahve an aggressive bust up, but neither of them seemed to lose the plot like that. I'd imagine the players can sense the nervous energy from him.