The hole in the pictured jig should have the same diameter as the diagonal measurement of the square stock that's to be made into a dowel. If you're feeding round stock through to make a smaller diameter dowel, just make the hole the same diameter as your stock. If you can't get the stock to turn easily, you may need a slightly larger hole.
The height difference between the table saw blade and the bottom of the jig hole will determine the final diameter of the dowel. Raising the blade will make it a thinner dowel, and lowering the blade will make it a thicker dowel.
If you want a formula, then your resulting dowel diameter will be:
Dd = 2*(Hh - Hb)
where
Dd is the resulting dowel diameter
Hh is the height of the jig hole center
Hb is the height of the blade
The source YouTube video shows the stock being chucked up in a drill and rotated as it's fed through the jig. For thicker stock, you may have to drive a 1/2" bolt into the center on one end in order to fit it in a standard drill chuck, or possibly just turn it by hand.