Note the different resistor arrangement around the triac! The Chinese design uses a capacitor to filter noise from the gate and to partially snub spikes from across the line. For driving a heater which is mostly resistive, the capacitor isn't essential but I would guess it is marketed for switching reactive loads too. You really don't want a 330 Ohm resistor sinking the gate current away.
My point about the LED in series with the MOC3020 is there isn't much headroom if, for example, a high brightness LED is used. An indicator type with Vf of ~1.6V will work but one with higher Vf probably wont. Most high brightness LEDs have a Vf of more than 3V and given that the Arduino output voltage will drop under load, there may not be enough current to turn the MOC on.