Going into the carousel you didn't rev match and caught 2 downshifts from 3rd to 1st. Not sure if you hit a false neutral and then tried to get it back into any gear you could (which happened to be first gear according to your gear indicator, I can hear the "clunk" of going into first) and then you let the clutch out pretty quick, your motor wasn't going as fast as your rear wheel at that point and the motor slowed your rear wheel so abruptly it caused a slide (nice save btw).
Rev-matching will help get the motor up to the speed that the rear wheel is going when you downshift and will help prevent slides. However I think most of the issue in this incident is that you went all the way down into 1st gear and let the clutch out quickly.