At a vehicle speed much smaller than the air speed it does not matter if one subtracts the vehicle speed. At zero vehicle speed your (wrong) formular gives the full power theoretical power in the wind, and this is not the power actually captured. A sail is not at all 100% efficient in converting the energy ! Going against the wind actually needs extra power, while the could provide power if used in a different way. At zero speed the efficency is zero.
When the vehicle moves at the speed of the wind it does not matter if w-v or v-w is used, both would be zero. So even if the sign is wrong it would not make a difference at that point. When using the correct formular for the power, there is (w-v)² * v and in the square the sign makes no difference.
That is potential power if you want so it will not do any work but as soon as vehicle moves it will do work.
Obviously at vehicle speed zero w-v or v-w will make no difference other than the sign of potential power showing direction in witch the power can be used if you start moving.
The sign is important as it will show if vehicle accelerates or decelerates and w-v is correct as it will show vehicle can accelerate when vehicle speed is below wind speed directly downwind while using v-w will mean vehicle decelerates while vehicle speed is below wind speed and that will not match any real experiment.
The reason Derek decided to use v-w was to show there is available wind power when vehicle is above wind speed but he needed to use a wrong formula to match his wrong understanding of how the vehicle actually works. Vehicle is not powered by wind directly when vehicle above wind speed (that will be impossible) but it is powered by stored energy.
While that energy that was stored is still wind energy since it is stored energy it will get used up by all the vehicle losses so any real vehicle will slow down after that is used up.
Vehicle is in touch with only two mediums and those have a relative speed of wind speed - ground speed so basically wind speed since that is referenced to ground.
Vehicle weight 100kg vehicle sail area 1m^2 only allowed to drive directly downwind
Relative to ground 0m/s
Wind speed 10m/s
Vehicle speed 0m/s
Potential wind energy in this above mentioned conditions will be
0.5 * 100kg * (10)^2 = 5000Ws = 1.39Wh and this is the max kinetic energy an ideal vehicle can get to since potential wind energy will decrease and vehicle kinetic energy will increase.
How come nobody answered the time it will take such a vehicle to get to half the wind speed so 5m/s ?
To be able to correctly answer this question you will need to understand the relation of vehicle speed to available wind power.
I'm sort of an expert in this because I work (my hobby also) in renewable energy storage so I investigated all types of energy storage available and also designed my own wind turbine many years ago. I ended up not using the wind turbine as solar PV made way more economic sense even with relatively good wind resources at my location.
I have designed my own net zero energy house and so both electricity for appliances and heating are supplied by PV solar with energy storage in LiFePO4 and thermal storage in thermal mass (LiFePO4 cost amortisation is around 20cent/kWh while thermal storage is just 1cent/kWh).
I'm not an expert in all area of physics but I have large amounts of experience in energy storage of any type and renewable energy generation.