Why can't this circuit work for an inductive load?
See this AC PWM Dimmer for Arduino article on instructables,
which says:

problems start, because he is feeding the gate from the MOSFET, with a voltage that is shorted by that same MOSFET. In other words, if the MOSFET is fully opened the DC voltage coming from the rectifier is completely shorted. Therefore there will be no voltage anymore to put on the gate and the MOSFET will block again. This effect might not be so outspoken by a low dutycycle (= lamp on a low intensity), because of the presence of C1, that will retain its charge for a while and will be receiving new charge thanks to the low dutycycle, but at 25-80% dutycycle the voltage on C1 just cannot be sustained anymore and the lamp may start to flicker. What's worse is that at moments that the voltage on the gate drops, for a while the MOSFET will be still conducting, but not be fully saturized: it will slowly go from its nominal 0.04 Ohm resistance to infinite resistance and the slower this goes, the higher the power that needs to be dissipated in the MOSFET. That means a lot of heat. MOSFETS are good switches but bad resistors. They need to be switched ON and OFF fast. Currently the circuit heavily relies on D1 to keep the voltage on the gate of T1 at acceptable limits while the voltage is swinging between 0 Volt and Full peak At peak the rectified voltage is 230x1.4=330V The average rectified voltage is 230x0.9=207V
If we forget about the smoothing effect of the capacitor for a while and presume the optocoupler to be fully open the average voltage on the capacitor would be 22/88 * 207 =52 Volts and in peak 22/88 * 330= 83 Volts. That it is not is because of D1 and the fact that the MOSFET will short the Voltage.
If the optocoupler is not in saturation and its impedance therefore infinite, the capacitor C1 would charge up to full rectified voltage if not for D1. On average 3mA will flow through R3,R4 and R5 (207-10)/66k which equals a power consumption of 0.6 Watt in the resistors R3,R4, R5