So you are not really a rider at this point - you're a passenger. Horse is going pretty much where it wants to, video shows horse moving left/right (just a little) because you don't know how to ride and you are loosing your balance. (Horse is trying to stay underneath the person on its back - so when you start to fall left horse steps left to try to keep you from falling off - horse is a saint!)
Lessons would probably help a lot but bearing that here's my take:
1.) Stirrup leathers are too long (as someone mentioned). That means you are on your tip toes trying to retain the stirrups. Insteand sit in saddle and adjust leathers so the stirrup irons hit at or above your ankle bone. If you find you are still having to do the tip toe thing shorten leathers until you can put irons on the balls of you feet and push heels down.
2.) Shorten reins. Right now horse has all the control, you do not. Reins need to be short enough so the instance horse tries to turn, etc. you can prevent it from happening. Also do NOT just use reins to steer - use your legs also. If you want horse to turn left then in neck reining you lay right rein against right side of neck and SLIGHTLY weight inside stirrup. If horse doesn't go left then move right leg back a bit, if still no turn push with right leg - weight and legs are at SAME time as neck cues.
3.) Sit straight up and down with weight down thru heels (think of standing in stirrups and sitting down on butt - your leg and body position should not change - only your heels should go down and your knees bend a bit. This is the proper body position.
4.) Elbows should be at waist. May have to move forward at time but VERY rarely back. If you move elbows behind your waist then reins are too long (see #2 above).
5.) Practice walk/halt (sink weight into stirrups as you tighten reins to halt) then halt/walk (relax elbows and body and if needed squeeze (then release) legs.
6.) Once you can walk/halt/walk and turn without loosing your balance (suggest doing some of this is an enclosed area with your eyes closed as a test - and if you don't loose your balance you're starting to get it), then introduce walt/trot/walk. Then add in walk/trot/halt...until you can move between halt/walk/trot in any order and retain your balance and control of the horse. (Then add with eyes closed.)
7.) When you can do that you're ready to canter. Come back with another video and we'll see of we can help.
Good luck. You've got a great horse to learn on (mine would have left you in the dirt
- so take advantage of him/her to teach yourself how to ride. If you find the horse not doing something "right" look at yourself first - problem is almost always with the rider.