RCD snubber vs active clamp
But where is the resistor? Why is it needed in the RCD version and not
  in the active clamp?


In the passive clamp, once the capacitor has stored the excess energy from the flyback transformer's primary leakage inductance, the diode that feeds the capacitor becomes reverse biased and hence the capacitor remains charged (unless a discharge path is provided). If a resistor wasn't added in parallel with the capacitor it would remain charged and the voltage on that capacitor would "staircase" up over several switching cycles to a point where it no longer provided protection for the switching MOSFET and the MOSFET would die.

For this reason, a discharge path is provided in the form of a parallel resistor hence, the excess energy is burnt off.

With an active clamp, the added MOSFET is used to both route the excess energy into the capacitor (as per a passive clamp) and then return it to the primary inductance and thus, the energy is conserved.