I've been thinking about this more and it is interesting. There's always something to be learned from cheaters.
I don't think this has anything to do with capturing energy from descents to use elsewhere. I'm pretty sure they're using the bottom-bracket crank drive I linked earlier in which the motor powers the cranks and then the wheel through the chain and gears. In this case because of the freewheel mechanism there's no means for the wheel to act on the motor to use it as a generator to put power into a battery. Since the rider can't slow the bike by turning the cranks backward the motor can't recover any energy from the bikes movement either. Regenerative braking can be done on electric bikes but it needs a hub-based direct-drive motor in which the motor is directly connected to the wheel with no freewheel mechanism. In essence the motor basically is the wheel (look up direct drive hub motors if it isn't clear). With this setup you can either put power into the motor to use it as a motor, or with the bike moving the motor can be used as a generator to recharge the battery. If you neither power nor regen the motor (ie don't do anything at all) the motor simply acts as a constant drag source due to magnetic drag.
Incidentally this regen technology is still quite new and experimental on electric bikes and isn't widespread like it is on electric/hybrid cars. The bigger issue is that regenerative braking is only a benefit if you had to slow or stop the bike anyway. If you're rolling down a hill on a bike and then the road levels off and you intend on continuing, I can't see any benefit from activating regen on the hill versus letting the bike continue to pick up speed and using the momentum to carry the speed along the level part. I'm speaking in generalities here but with regen you have to convert the kinetic energy of the bike to electrical energy (losing some because the motor/generator is not 100% efficient) and then that electrical energy has to go through a converter (because the motors used on these bikes are 3-phase brushless and produce/consume AC power while DC is needed/produced for the battery, the conversion is not 100% efficient either) and then you lose a little more because battery charging is not lossless, after all this only a portion of the energy you recovered from the braking has ended up in the battery.
When you come to use that power, the process works forward with some power being lost in the converter/motor controller and then more in the motor. If instead you let the bike roll you will also lose energy due to rolling and air resistance although depending on the speed that may well be better than trying to regen on a downhill. And if you do regen on a downhill the bike is going to immediately slow down anyway, so bottom line is you're not able to get something for nothing. Now there's certain situations where regen braking on a downhill makes sense, like if you want to maintain a constant speed, and instead of dragging a mechanical brake you put that excess energy into the battery. And if you know you need to stop, again you can put (some) of the kinetic energy you lost from slowing into the battery instead of it going to heat in the brakes. Also kinetic energy goes up as the square of velocity while power required to fight air resistance goes up with the cube so it may be better in some situations to activate regen on a hill if this saves energy overall compared to the bike hitting terminal velocity due to air drag....
...alright, that was longer and more full of technospeak than I intended, so the point is they're not using regenerative braking to cheat. Actually I wonder if regen braking really is cheating since you're only recovering energy you ultimately put into the bikes movement yourself one way or the other. Okay back to this 'mechanical doping':
It appears it is as simple as using a small concealed motor and battery to assist the rider. Again they are not using the motor exclusively to power the bike, the rider is at all times putting in effort as well, but versus their competitors on unpowered bikes the rider of the cheat bike is going to be using a little less power of their own which in these sorts of races allows them to win. It would be far too obvious if the motor was putting hundreds of watts through the cranks, much more subtle if it's just a little here and there. Who's to know it's the motor that's allowing the rider to edge ahead and not just the rider having a good day or the competitors just being a little less fit maybe?
This sort of thing would be unthinkable a decade ago because of how poor old style batteries were (nicads, lead acid). Thanks to lithium batteries you can now stuff a lot of energy into a small and light package and draw it out quickly as well. Take the
battery I use on one of my RC planes:
It holds about 25 Wh (Watt-hours) of energy, weighs ~200g and fits in the palm of your hand (or neatly in a bike frame I'd bet). With these batteries you can get practically all that energy out with very little loss so all that 25Wh is available. Let's say you need some 'assistance' on the bike for half an hour and the battery>controller>motor efficiency is 50%. That gives 25W of power constantly for that half hour. A cyclist might be putting out 100W by themselves so that's an extra 25% power right there. Not just for a short burst, but for the full 30 mins more or less (power drops off slightly as battery is depleted).
There's batteries with better energy density than that and motors/controllers that are better too. You could easily have an extra 50W of power (mechanical power, after losses in the motor etc) on hand for an hour. That's going to massively benefit you against your competitors alright.
