The free body diagram for the yo-yo is drawn in the video but let us repeat it here (this is for the tension from underneath).
How we do we know which way it will go? We need to determine in which direction the net torque is. But torque depend on your choice of pivot. So which pivot should we choose? The natural pivot is the center of mass but then the torque from the tension and the torque from the static friction are in opposing direction and its unclear who will win.
If instead we choose the pivot to be the point of contact, then only the tension has a non-zero torque. It is CW with respect to that pivot and the wheel must go right (on the images, the actual demo went left because it was turned around).