Kusenko, who conceded the bet to Veritasium's Muller, only conceded that if you accelerate an object to wind speed and then the wind suddenly dies, your (low-drag) vehicle will continue downrange at a speed greater than the (now zero) speed of the wind on momentum alone.
That technicality, however, is a complete misunderstanding of how the vehicle works. The designer of the vehicle, Cavallaro, apparently only built the vehicle to prove the soundness of the physics to doubters, according to the narrative given by the Veritasium video. That designer offered a second $10,000 bet to Kusenko presumably simply excluding the technicality that Kusenko 'lost' to.
It would be a simple bet: that the vehicle can accelerate to and sustain a speed faster than any momentary peak wind speed during the race. Since the vehicle can reach 2.8x the wind speed, all it would take is the vehicle doing so while no gusts exceeded, say, 2.5 the average wind speed during the run.
The actual explanation, which apparently still escapes Kusenko:
If the wind speed is 10 knots from west to east, then this vehicle can accelerate to 10 knots going east by drag (east) alone. At that speed the apparent flow of air (from the reference frame of the vehicle) is zero, and so the drag (east) force on the vehicle is also now zero. At that point, you can rob energy from the wheels (manifesting as increased rolling resistance or west drag) to drive the propeller. This increased rolling resistance doesn't slow the craft, as long as the total rolling resistance is less than the drag force of the wind pushing us forward.
We use this energy to rotate a propeller to push air to the west. From the stationary/ground reference frame, the propeller will have the effect of slowing the airflow behind the vehicle from 10 knots relative to ground to 0 knots relative to ground. This energy -- robbed from the air -- pushes the vehicle forward (east) by Newton's third law.
The counterintuition is that the energy that pushes the vehicle forward is robbed from the wheels, i.e. from the vehicle itself. It's correct to understand that the acceleration from such a scheme would be (at best) a net zero.
The vehicle was already travelling at 10 knots, so the additional energy now being extracted from the wind makes the vehicle travel faster than 10 knots. Assuming the mass of the displaced air roughly equals the mass of the vehicle, this would get the vehicle to a total speed of 20 knots. As far as I understand it, you can then get the sqrt(2)~=1.4 multiplier from the pitch of the blades - the propeller blades do not face 'straight downwind' (perpendicular to the wind) but are angled. I think that this 1.4 * 2 * windspeed is what gives the 2.8 figure mentioned in the article.