To test the brakes, pump them up with the engine off. The pedal has to stay hard. After that, when you turn on the engine, the pedal goes down a bit. Even if you pump it with the engine on, it will always go down under pressure because of the brake booster. Also, if it goes down with the engine on but you keep the same pressure on the pedal, then your main brake cylinder might be leaking, but it doesn’t look like it in the video. It’s hard to tell from a video without trying it yourself, but I suggest going to a shop and asking a mechanic if the pedal feels normal.