Triac optocoupler circuit
You have to analyze whether the triac in the optocoupler can be triggered by the dv/dt, not just the power triac, before you can draw conclusions about the snubber. 

The 330 ohm resistor prevents leakage in the optocoupler from triggering the triac. Snubberless triacs tend to be fairly insensitive so you may not need that, but you can analyze the minimum trigger current vs. maximum leakage (probably at maximum temperature). You should try to keep the opto cool for lifetime reasons, but usually it ends up being mounted near the triac. In this case your triac is guaranteed not to trigger with 2mA gate current at 25°C Tj, and from Fig 7 we can assume that &lt;1mA will not trigger it even when hot. The optotriac leakage appears to be &lt;100uA at 100°C so I think you're fine without the resistor.