Essentials of Swing Plane
What you see in the video are the basics of swing plane and to be truthful, probably all you will need to know. A lot is made of the plane in teaching circles but given the huge variety of plane options seen on the world tours, there is clearly more than one way to view this topic.
Prioritise the Down Swing Plane
Where you see a large variety of back swing planes on tour, they generally converge into something more universal during the downswing. If If you are going to err one way more than another in the back swing then a plane that is too steep can shallow in transition in what is a fluid and dynamic change of direction. A flat plane has to swing over the top to find contact and that is less desirable.
Every golfer pulls and torques (twists) the club handle differently in the downswing
A paper by Mackenzie (cite) modelled the swing plane options and came concluded that a downswing that either re-traces the upswing or shallows beneath the up-swing is significantly more likely to square up at impact. Conversely, a steeper downswing is fighting against the forces of the swing and is less likely to line up to the ball.
Once again, the circle drill is a really useful way to conceptualise swing plane and helps create the right internal representations. Just be aware that there is a lot more arm rotation in the circle drill (top stage) than in the swing itself. The swing at ground level will require more vertical lifting of the club and less arm rotation.