You are quite a neat little rider, however you are very much a passenger.
I don't think your horse moved terribly, he's just very much on his front legs. When a horse is on the forehand, it gets unbalanced and often the canter will start to become 4 beat, and the hocks unable to bend.
I'd like to see you sit right back over your seat bones, bring your upper body back. Think of making yourself look like a capital "D" - your spine being the straight line, while you push your belly button towards your hands.
Another one, is to imagine that you are sitting on his haunches when you ride, and you're about to drive up a bridge. You need to lift his wither up, and lower his haunches. Press his haunches down with your seat bones, and lift his wither with your belly button.
Pin your elbows back so that they rest on your hips, and allow them to act as hinges. Right now, your whole upper body is doing the work of your lower arm. The elbow is a hinge, that allows your lower arm to follow the movement of the horse's topline while your body remains still. Try resting your hands on your horse's wither, or slip your pinky fingers into the velcro on the front of your saddle pad, a neck strap, or a monkey grip. This will give you just enough movement through your forearms to follow the horse's movement.
Just these two corrections should start to bring your horse a little more over his haunches. Getting your seat stable should be your number one priority, you really need to be on your seat bones and driving the horse forward and up rather than being a passenger and allowing him to nose dive.
Also, I would avoid doing that much canter. You are riding around and around and around and I did not once see you adjust anything. If that were me, I would have ridden at least 5 transitions on that sized circle, would have ridden collected-medium-collected canter, asked the horse to bring its jaw and poll an inch to the inside, then straight, then an inch to the outside, bring the quarters in, push them out, ride leg yield on the circle etc.
Shake it right up, going around and around and around and around and around and around.... does nothing productive other than getting the horse fitter and especially when on the forehand, you'll be building up muscles in the wrong places, that will take a long time to undo.
So, sit back on your seat bones to lift the wither, elbows locked onto your hips, hands together and at the wither, using elbows to act as hinges, and SHAKE IT UP :)