Now after I read that the copilot flew, I am very convinced that this is what happened: she struggled to get it back to the centerline and – helas! I made it to the touchdown! – released the control inputs (you see NO lateral input on the video or picture after touchdown). Once the upwind wing rises, the wind pushes the airplane sideways, I doubt that here was any “additional” gust.
As 3.500-hrs A320-Cpt I can only confirm what md4490 and Right Engine state: in strong crosswinds, an Airbus must be landed like any other airplane, since the physics are the same, and it works (hold that upwind wing down!)