I have a few comments,
1. Way too many false casts. Every time you false cast, there is an opportunity to introduce a timing error that may causes a tailing loop, line sag, etc.
2. Stroke path, length of stroke and timing are almost identical from cast to cast. That tells me that you are not lengthening your casts very much between strokes. It also tell me that you are not adding much energy with each false cast. The purpose
of a false cast is to either add length OR change direction and you are not doing either. This has to improve to add distance.
Try to improve by lengthening the stroke path and acceleration with every cast, not only on the forward cast but the back cast as well. You can do this even without a double haul.
3. You start each cast with the rod position way too high. For example at 1:40 min you end one cast with the rod held at about 10:00 but you never
follow the line down to the water. Your then take in line, but instead of stripping the line with the rod tip at the water; you strip the line in and at 2:00 min you begin the next cast with the rod at 10:00.
That line sag from the rod tip to the water is a big energy waster. So follow the line to the water and begin every cast with the fly line straight on the water (remove all slack). This alone will improve your cast. Report back and tell me how this single change made a difference.
4. As Jackster said learn to double haul and initially make the hauls short enough so you can feed the line back. Long hauls will cause beginners to be unable to feed all the lines back and they will mess up the timing. Begin with about 12 inch hauls.
5. Do not let go of the line when you shoot line. The Tom Rosenbauer illustration shows the caster letting of of the line, but this is only when you want the maximum distance. Shoot line through an "O" ring made with your fingers of your line hand as shown below:
6. When your learn to double haul and shoot line, you will be shooting line on the forward cast alone. 99.99% of caster do this. If you really want to cast far in the shortest number of false cast, shoot line on the backcast and the forward cast.
7. Here are some videos and articles to give you a start:
Joan Wulff: The Double Haul
Tom Rosenbauer Double Haul