I’ve generally taken the “more bees with honey” approach when managing people. That’s not just because it avoids disruptive conflict which can drag on with both the person and others that may take their side in the dispute, but because it has been my experience that those types of interactions can lead to observers (often team members and/subordinates, but sometimes customers or other interested parties) losing respect for you. And loss of respect has a much more detrimental effect on the group as a whole, the enterprise, and your ability to effectively manage in the future.
I have certainly told people off before, but I can only remember going as far as Vinny does in that clip once, and I regret it to this day, as I almost immediately realised it was a shite thing to do and it was going to make things much worse overall. And it did just that. The employee ended up quitting two months later, miserable the entire time before, and others on the team noticeably interacted with me differently afterward, often afraid to give me bad news or reluctant to offer opinions for fear they would be on the end of one, as well. I eventually left the position because I realised the majority of the team was never going to see me as the manager I was before the incident. It was early on in my professional career, thankfully, but it was a hard (but incredibly valuable) lesson that I took with me in all work I did after.
As you and others have said, we don’t know what came before this and I tend to agree Burnley included that unflattering clip paired with that specific section of his interview for a reason. Gudmundsson could have been moaning in and outside of training regularly, Vinny could have tried taking a more quiet approach, the player could have been having a ‘Cancelo effect’ on the team, and that day was just the final straw.
I played football through my early 20s and have had coaches that took that approach a lot. You do tend to get over it quickly most of the time as a player. But I never found that approach to be more effective than a mostly more considered, personal approach. And I do wonder if that way of managing could actually be consistently effective in modern football.
If I am being honest, I think even Vinny would admit the bit where he goes back for more at the end was not his finest hour and did give the impression of him no longer being in control.