Sail propulsion (or wing lift) by wind deflection (without Bernoulli principle)?

I give you a possible explanation of the experiment in the video. If you look at the picture below, I have drawn the trajectory of a gas molecule which hits the sail. How you can see from the force scheme, when the molecule hits the sail then a force (N) acts on the sail and of course the same force acts on the molecule. The x-component of the force N on the sail accelerates the sail on the x axe, while the y-component is balanced by the constraint. You should also consider the impacts of the molecules on the other side of the sail (leeward) that generate a force in the opposite direction. If $n$ is the (constant) number of molecules which hit the sail on leeward, it will depend only on temperature $n=n(T)$. Calling $m$ the number of molecules which hit the windward, you have the net force on the sail on x axe: $$F_{x}=mN_{x}-n(T)$$.

You are wrong in your statements about the videos:

1. It is misleading to say that the "wind comes from ahead", it comes from the starboard (right hand) bow at a marginally steeper angle than the sail; that angle is critical.

2. The air blast is aimed at the leading edge; it is passing both sides of the sail.

3. What telltales? I see none.

The sail is acting just like an aeroplane wing; air passes around both sides and is deflected backwards. There are several principles involved.

First is the simple "bouncing molecules" model given in one answer. This model can only account for well under half of the lift generated. The leeward path is longer than the windward path so Bernoulli does apply to some extent, but again not enough. Circulation theory gives a fuller description of how wings work, but it's complicated. Ultimately, by deflecting the air backwards and slowing its sideways movement, Newton's laws require an equal and opposite reaction on the sail, pushing it forwards and sideways. The wheels resist the sideways force, but not the forward one.