Most planes either use automation or have a manually added fudge factor to account for gusty winds. For example an Airbus automatically adds 5 knots to the minimum approach speed (which itself is 1.3x stall speed in general terms) for a given approach. Book procedure is to increase that buffer by 1/3 of the gust value over the steady wind if 1/3 exceeds 5 knots, but not to add more than 15 knots. So if the winds are 10 gusting 30, then the gust factor is 20. 1/3 is roughly 7 knots which exceeds 5 knots so we’d manually add that to the minimum speed.
Additionally, some aircraft take the steady state wind, and add it to the derived approach speed above in order to maintain a constant ground speed and energy level. So if the approach speed is 138 knots and the steady state wind is 10 knots then the plane will try to maintain 148 knots of airspeed to keep a ground speed of 138 knots. This is called ground speed mini (minimum) in Airbus world.
In more pithy terms, yes, a drastic falloff could cause the plane drop. More so if it’s already near its minimum approach speed.
It looked like they never flared or flared very late to me which is not overly uncommon in low visibility conditions or semi white outs. The visibility didn’t look too bad from the video above, but keep in mind that the pilots are looking down through more air than the observer on the ground. They’re essentially staring down the hypotenuse of a right triangle whereas the observer is looking down the base leg. This is called slant range visibility.