This video highlights the fact that the friction between two surfaces increases if the two surfaces are pressed more strongly into each other. (f=μN)
For example, the grip that the stick exerts on the beans (f) is large only if stick is wedged tightly among the beans (leading to large N).
Same thing for the paper. Only if the paper is pressed hard horizontally against the stick will the vertical friction be large enough.
When we “pin” papers on the fridge using fridge magnets, it is not the magnetic force that holds the papers in position. In fact, the magnetic forces do not even act on the papers. What the magnets do is to ensure a large normal contact force , which then allows for a large friction.
Lastly, note that in all the examples in this video, friction was the force that resulted in motion. It is a common misconception that force opposes motion. This is wrong. Friction opposes relative motion between two surfaces, not motion per se.