The video does not play very well for me - it is very jerky and looks almost as though it's in fast forward!
They didn't make it easy for you though - no chains/poles/fence to line the arena?????? That makes it very difficult!! - You can see that everyone has problems with straightness, the lines worn into the grass are very curvey ;)
Keeping your hands low is good at this point in your rising is good, you want to feel the wither and base of the neck, to follow the topline with your elbows. Keeping the hands to high will often result in a broken contact if your seat is not 110% perfect.
What I can see, and I think I'm accurate in this, not just the shakey video - but it looks as though your elbows are locked. This will create a loop, then tension, then loop in the reins, which then encourage the horse to duck back behind the bit and come into a false frame. Imagine that you have weights tied to your elbows, they need to just 'drop' at your sides, try to stick them to the top of your hips. This will free the joint up, and allow the elbow to open and close with the movement of the topline.
Once you master this, you will find that you horse is more willing to come into your hand, and your scores will improve.
You did a very good job of riding this test, it was a pleasure to watch - very tidy and soft. I think maybe, without seeing the other competitors, they had their horses up and travelling a little more. Your horse goes very nicely, but is a little flat and 'nice'. If you can get him up and travelling, a bit more active and uphill, you will find that your scores will increase.
You have made an excellent start though and I hope your trainer is proud as they have done a good job!