He definitely has something going on in the hindend. I can't tell what. I definitely saw a few bad steps in the video and it looked to me like he was struggling a little to keep in a headset. Plus he did some tail switching.
Just based on him being slightly off, I would pass. If you are really interested in him I would like to see him moving on a very loose rein. My guess is he is trying very hard to do what you ask (and be collected) but whatever is wrong may be more pronounced when working freely.
I've been looking for a horse to free lease for the past 2 years. The first horse I looked at had a stifle problem. I went to clean his hooves and he could not even lift his leg as it was completely locked. He bucked under saddle, so I quit riding him.
The second horse I went to free lease, did really well walk-trot. She also bucked under saddle. According to her owner she has stifle problems and the vet said she has loose stifles. If she bucks on the lunge, they know not to canter her that day. I did notice she felt a little stiff right before her bucking spree.
I would not consider either horse "sound". The first horse was already being ridden on a daily basis and was in excellent shape, yet continuing to have stifle issues. The second horse may or may not get better with consistent work.
I decided to pass on both "free" leases. My mare has some soundness issues, but at least she doesn't decide to buck!
I definitely don't believe "getting the horse fitter" is an absolute cure to stifle issues. Keep in mind some horses with stifle issues go on to need surgery, or could have OCD lesions or chips in the stifle.
If it were me I would be running away from purchasing that horse! Although if you are really interested a vet visit to make sure it is not something else that is treatable, may be in order.
It is concerning that you think the horse "might" be drugged. Considering how horrible my luck has been with lameness issues, I would pass by this horse immediately. A young horse that is sound can be schooled, but an older horse with lameness issues may never be able to perform at the level you want.