Question regarding a resistor in optocoupler/TRIAC circuit
The 100\$\Omega\$ resistor may help prevent the triac from triggering with high dv/dt (for example, with a somewhat inductive load- which you have with a motor load). It's generally not necessary unless you are using a sensitive-gate triac. For motor loads you should consider using an alternistor (Edit: which the BTA16 is), which has higher dv/dt immunity. 

You did not ask about the 600\$\Omega\$ resistor, but increasing that part value from the minimum will cause unnecessary EMI and possibly other problems.