The diagonal force is very important, especially when there is no splitter or riving knife on the saw. That diagonal force, is in towards the fence in order to keep the workpiece registered along the fence the entire length of the cut.
You should really re-evaluate your direction of force when using a push stick/shoe. Never use the stick/shoe to apply lateral/diagonal force toward the fence. Why? Because as you are applying force to the board toward the right, your hand is experiencing counter-force toward the left...toward the blade!
In other words, if something goes wrong and the shoe slips, your hand will already have the propensity to move to the left. (The shoe will rotate to the right, like slipping on a banana peel.)
If you need lateral force, that is where a featherboard comes into play.
For similar reasons, I never use a push stick when the cut is wide enough that the push shoe is not riding directly against the fence. When my push shoe is moving past the blade, 3 or 4 of my fingers are sliding along the right side of the Unifence. If you are using a Biesemeyer fence, then the best shoe is one that wraps the fence like your video showed.
A few years ago I was called as an expert witness for a tablesaw injury case in British Columbia. The case hinged on the over-use of push "sticks", and the oporator's right hand moved into the blade. The operator wasn't in control of the workpiece, his push sticks (2 of them) were in control. The diagonal forces permitted his hand to drop down onto the spinning blade. (I replicated his cut with a live blade for photo purposes, and I was terrified the entire time.)