The other thing about this...it’s so banal.
IF you had a valid means of generating power and synchronizing it with the grid, there’s no reason why you couldn’t feed it back into the exact same outlet you extract it from EXCEPT at some point the “output” cable of your generating device would be “hot” with a “male” plug which is a decided no-no. Answer: leave it plugged in all the time or hard wire it into yhour home system, perform the on/off line switch with a real switch (elswhere) like we do with all our other devices.
But what’s typical about this idea from the standpoint of how well it’s been thought out, is that it’s a fifth-grade level deal. Look, for example, at the size of the wire coming out of the plug. (Yes, I know, it’s only an artist’s rendering) but it’s BS = BarackS**t.
What these solutions typically ignore is that the overwhelming use of energy is for heat. The exercisers should try heating a house with their breath and body heat and see how far they get.