When you hear her saying it it sounds incredibly threatening and unpleasant.
Something else that isn't really getting enough weight is that a teacher was saying this to two children. If this happened to me as an adult I'd be pissed off and maybe upset, but I'd have the ability to escalate and I would expect to be treated fairly. I would know that I had certain protections, either by law, HR policy or whatever.
At 13 if I'd had a teacher saying that to me I'd have been incredibly upset and worried about how this would come back on me. Would I get into trouble? Would my parents be hauled in and told about what I'd supposedly done? Would I have to change schools?
The girls clearly suspected that they wouldn't be believed - and I would put good money that if they'd just relayed events verbally that they wouldn't have been - hence the recording. The teacher accused them of saying things they were adamant they hadn't (the "asylum" comment), made threats, made personal comments (the use of the word "despicable") and therefore I would say she has abused her power over them. This could so easily have escalated into an entirely unfair 'teachers word versus theirs' disciplinary issue against the students.
That they had the foresight to record it is to their credit.