I spent a lot time trying to draw the collision shapes, expecting to see cyan lines or red dots or some sort of feedback showing me the shape of the polygon I was drawing. I finally realized that Godot gives no feedback at all that anything has happened until you have finished clicking all four corners and clicked back on the first corner to complete the polygon shape.
Watching the video again, this is perhaps obvious. At 10:26, Yann clicks each of the corners and the interface gives no reaction until he completes the shape. If you make the grid size smaller than the tile (as he does for the next tile) then you can see the inner lines of the shape that is being drawn. However for the 64x64 grid any lines being drawn are indistinguishable from the lines that separate the tiles.
Again, maybe this is obvious, but it tripped me up for long enough that I wanted to offer this tip for anyone else who is having trouble drawing their collision shapes.