How does the canard plan of the Dassault Rafale work?
The answer is in two parts. First, at higher speeds, control surfaces have more air moving over them and so they don't have to angle as much to provide the same force necessary to move the jet as they do at slower speeds. In fact, a thin control surface like this canard will stall at lower angles of attack than a thicker profile would (the thinner profile reduces drag which is why it's used here), and a stalled surface can't do its job.

Second, modern jets like the Rafale have fly-by-wire systems with flight limiters, to avoid the pilot overstressing the airframe at high speeds. The first video shows the Rafale in landing configuration, approaching a carrier at maybe 150kts. The second video shows high-G maneuvers at probably between 300 and 400kts. The forces at play on the canard are, in general, related to the square of the speed of the air moving past them, so if the system allowed the canards to present the same angle to a 300-knot flow as a 150-knot flow, all other things being equal the canard would be under 4 times the stress. At 450 knots that canard would be under 9 times the stress. Very quickly you would exceed the mechanical strength of that canard surface entirely, and then you wouldn't have a canard surface at all. So instead, the canards are moved at a shallower angle, with the difference in pitch rate, up to what the flight limiter will allow the entire aircraft to do, is made up using the elevons on the wings.