M2 work energy power problem

Is it not the case, that the work done by the resistances produces the energy loss?

I am finding that part confusing- because in the questions work done by resistances= energy loss, but in this example that is not the case why?

This only applies when you have a closed system. i.e.when no energy is added to or subtracted from the system. In that case you simply have a change of state, in which the energy of state 1, E1, is the same as the energy of state 2, E2.

E.g. an object at the top of the hill with zero velocity has PE only.
If it now moves down the hill, with no resitance to motion, then its KE at the bottom is the same amount as the PE it has lost.
If there is resistance to motion, then you have to take that away from the PE and the energy left is the KE for the object at the bottom.

If your cyclist were simply free-wheeling down the hill, then the system is closed and you can do a simple energy balance - here the work done, on the object, would be the energy loss due to resistance, ER.

E1 = E2 + ER
ER = work done = E1 - E2

However, if the cyclist is pedaling, then he is adding energy to the system (which simply consists of himself and the bike) and the energy balance would be,

E1 + work done = E2 + ER

HTH