The aircraft basically stalled out in a dive, and with no cohesive airflow over the control surfaces, the aircraft continued to stall to the point of impact.
What most likely happened was was a loss of situational awareness in the pre-loop dive, resulting in a steeper and faster dive than intended.
That's just... such a marginal thing. It's like complaining your supercomputer melted because the CPU got 0.1C too hot. Like - it's technically possible, but if it's that close you were already way way way past safe and sane margins.
There's control lockup, where the aircraft is flying so fast that the mass flow of air over the control surfaces is so high that the controls "lock in place" or "get stiff", meaning the force you can apply to your rudder stick in the cockpit isn't enough to overcome the forces acting upon the control surfaces.
Then there's control compression, where the airflow around the wing is so fast that the local airflow around the airfoil becomes supersonic (aircraft as a whole is still subsonic) and detaches after the point of maximum airfoil thickness, leaving no laminar flos for the control surfaces to work with. This will feel different in the cockpit, instead of the controls becoming stiff they get loose but no control authority is achieved because your control surfaces are in fully turbulent flow.
Both of these phenomenon were a big issue in WW2 during dive attacks, since enocuntering or even going beyond the max aircraft speed was common during dive attacks, you wouldn't be able to pull out of the dive and go straight into the ground at very high speed. Either of these could've been an issue for Anders.
TLDW: the likely cause of the crash was low-level aerobatic maneuvering at an altitude of 700 to 1,000 ft, which is too low for such maneuvers. The pilot may have attempted a split S maneuver (see https://en.wikipedia.org/wiki/Split_S - aileron roll followed by a half loop) without getting the nose up high enough, ending up too low. It appears that the pilot had control of the airplane on the video, it wasn't stalled.