Hi there,
With 300 ohms in series with the gate with a triac that takes 50ma to turn on the line voltage will have reached roughly 15v and that is about a 2.6 degrees firing angle. Now 55us later say the triac turns on (a slow triac). That's roughly another 1 degree which means the line voltage will have reached about 20v, and that means the gate will now see about 67ma, and then the main triac turns on and shunts the voltage so the current drops to zero. That sounds pretty good to me.
On the other hand, without a resistor it is very hard to determine just what the current will be because we dont really know the dynamic resistance of the gate. Yes, it may work or it may work for a while and then blow out. That means we would be taking a risk.
If you read the second part of my signature line, "One expert specification is worth a thousand tests", that makes a lot of sense when we look at the data sheet for the device, where the experts who have already taken the time to specify this part have determined that a gate resistor is necessary. Thus, that's the best reason to use one and not take the chance of not using one. Additionally, they specify not a 300 ohm resistor but a 360 ohm resistor, which BTW handles the possible peak voltage better than a 300 ohm resistor which keeps the peak current in the device below the specified value of 1 amp at all times.