On your video the battery was turning the engine over well fast enough to start if all else good, as I mentioned earlier, almost too fast.
If it was the key you would have seen a lock sign or similar on the dashboard.
Do you have a friend with a diagnostic tool that can plug into the cars EOBD port to see if any error codes stored?
What is the history of the car, age , mileage, regularly serviced?
The one I mentioned before was a second owner Ford Fiesta, kept in a garage, with 30K miles from new and bought from the local Ford Dealer but still had low compression.
I also had a customer with a 3 cyl VW Polo they inherited from their daughter, it used a lot of engine oil and if allowed to get too low even when oil topped up it wouldn't start, until I did as mentioned on the other vehicle, many cars have high oil consumption due to their "short stroke" engine design,Toyota Yaris is another, where they get there power from higher revs, this means the piston rings need to seal really well to keep high compression or they will not start.
Are you able to do small jobs on your car or are you reliant on a garage?
Not recommended long term but have you tried using "EasyStart" spray, if it started right away it may be a clue or indication.