All the wheels only toys where air is not involved are the equivalent of that direct upwind version of blackbird using small capacity energy storage device maybe charging in a few ms and then discharging triggered by stick slip hysteresis either internally in the mechanism or externally at the wheels.
The wrong equation for power either drag or generation is what made the math possible without energy storage. If the correct equation for power is used then is clear from the math that neither direct downwind faster than wind nor direct up wind at any speed is not possible without energy storage.
The wheel based versions can be interpreted both ways. It is just a question on which plane is identified as the ground or "wind". It is somewimes a bit trikcky to look at the same thing with different referene frames, but this a major point of doing though experiments.
Quite some wheeled models may show some slip stick like action, but this does not say that this is essentially for them to work, there are some with little visible slip stick.
The equation for the power from a sail vehicle is not used in the calculatoins for the backbird at all, as there is no sail involved, only an active driven prop. So there is no need and no sense in using the equation for a sail dirven vehicle.
Trying to use the equation to show that the blackbird vehickle would not work also makes little sense, as at best this would only show that with passive sails it would not work downwind. This is accepted and one would even get the some conclusion with the wrong (w-v)³ type form and the correct (w-v)²*v type form. However this does not proof that a different type of vehicle could no work - it just does not apply.
To proof that the backbrid vehicle would not work the way would be to calculate the power available from the wheels and the power needed to drive the prop. If the prop needs more power than the wheels can provide, it does not work (at least not without energy storage or other methods not inlcuded in the model). So this already quite close to the calculation in the video. Just need to calculate (e.g. get an upper / lower limit) the power needed to drive to prop, so kind of the other way around from a wind turbine, maybe include the Betz limit or a similar factor for the prop.
People sees to like to use force for witch in most case they use the correct equation that includes (wind speed - vehicle speed)2 but then when it gets the time to calculate power they only multiply with vehicle speed instead of multiplying with (wind speed - vehicle speed).
Basically the wind speed is considered for force but ignored for power.
Not sure witch person did this mistake first but it seems it got everywhere.
There may have been other before, but the first to bring up the mistake here was electrodacus.
The form with (wind speed - vehicle speed)
2 only applies to vehicle speed < wind speed or would need to include the sign of (wind speed - vehicle speed), but at least it gets the low velocity range right.