I think these four different categories are not vocal types but vocal techniques. Every category includes exercises to practice every technique.
These four categories might still be one way to categorize singers. Because there seems to be no scientific consensus on categorizing singers or singing techniques, this categorization may or may not be better than other ways. To me they seem to be more like the building blocks to train yourself to a better singer. There are tons of vocal education videos online and I think it does not matter which of them you use if you learn to sing in a more healthy way with them.
One thing to consider is that (to me) these seem to concentrate on contemporary singing. I would listen to the exercises carefully and draw your conclusions based on them (example: in the exercise video Light Chest-No Chest Exercise Demo https://www.powertosing.com/light-chest-no-chest/ his voice "rattles" sometimes when he sings "nei nei nei nei nei", which is definitely not healthy)
High-larynx does not sound healthy to me. I have been taught it should always be low when singing in a healthy way. Falsetto is definitely a thing but not a vocal type, it is a technique (used by e.g. The Bee Gees), that may not even be learnable by every person.