Dan John is teaching the Hardstyle kettlebell swing. The purpose e of the swing, or any ballistic movement for that matter is the projection of force. The hardstyle swing should indeed be a hinge, not a squat, and the force should be projected outward (think broad jump), rather than upward (say vertical jump).
Knee flexion is an afterthought of hip flexion when it comes to the swing, but that's not to say we want those "drinky bird" looking swings. For girevoy athletes a utilize a higher a hinge with more flexion in their back for the purpose of keeping the load primarily on their extensors which fatigue at a much slower rate than your prime movers. But since the purpose of the hardstyle swing is force production over energy conservation, then we want to take full advantage of our prime movers and you have to find that nice middle ground where the optimal hinge position lies.
There are a few points of concern that I see with Dan John teaching the swing. I only skimmed the video, but I noticed he had his participants spiking the bell and overloading the eccentric before most of them were able to maintain a neutral spine - perhaps I need to rewatch the video in its entirety, but I would certainly never have a client overload their eccentric until they are able to hinge properly with a neutral spine.
Another note that must be considered with the swing, or any hinging movement for that matter (specifically deadlifts) is head position. Contrary to popular belief, cervical extension in the context of an aggressive hinging movement is not a great idea, as the effect trickles down to your lumbar spine. Extension in the neck leads to greater lumbar extension, and when they bones are in closer proximity this sends a signal to your saying "Hey we have structural (boney support) down here, so we don't need as much inner core activation".
This is concept often ignored that simply cannot be any longer. From my understanding, Dr. Stu McGill will be publishing some work very soon that demonstrates the enormous amount of shearing force on the lumbar spine during hinging movements performed with cervical extension.
The proper way to hinge is to maintain perfect crown to coccyx alignment through cervical retrusion and mild capital flexion. This may feel unnatural at first but with enough practice will be greatly beneficial to the health of your spine in the long run.