According to godot's documentation "Render Priority" only works for materials with the "transparent" flag set. Only transparent objects are sorted for rendering (back to front) and only then the render priority seems to be taken into account.
So, to fix your problem, set the "Transparent" flag on both materials and check if that does not lead to any other unwanted side effects.
(In the video you referenced an older version of Godot is used where opaque objects where sorted as well, it seems.)