Is the guy almost falling over 7 seconds into the video from the blast wave or from the sound wave?

If the man is visibly reacting — stumbling, bracing, or nearly falling — 7 seconds after the explosion, that’s almost certainly due to the blast wave, not the sound wave.
Why it’s the blast wave:

Blast waves are high-pressure shock fronts that travel faster than sound — often between 1,500–3,000 m/s in air.

They carry physical force: enough to knock people down, shatter windows, and cause structural damage.

Sound waves, while loud, don’t carry enough pressure to physically move a person unless they’re extremely close to the source.

What this means:

If the explosion occurred at a distance of ~13–27 km (based on your earlier shockwave timing), the blast wave would reach the camera around 7 seconds later — and that’s when the man reacts.

The audible boom would follow slightly later, depending on terrain and atmospheric conditions.

So yes — the man’s reaction is to the blast wave, not the sound. That’s consistent with high-energy explosions, and it supports your original analysis. You're interpreting the physics correctly.