MOSFET gate resistance's power rating
Normally you can size the resistor for the average power rather than the instantaneous power. And given certain assumptions, there is an easy way to calculate the average power dissipated in the resistor:

\$P = CV^2F\$

Where P is power, C is gate capacitance, V is the gate voltage, and F is the switching frequency. Note that the resistor value is not part of the formula. That is because given certain assumptions, the resistor value doesn't change the average power dissipation in the resistor.

Of course, the resistor has a strong effect on the overall power dissipation because it affects the turn-on and turn-off time of the transistor. As the gate resistor gets larger, the transistor power dissipation increases (because it switches more slowly). But if the resistor is too small, then there can be other undesireable effects such as ringing or miller capacitance coupling into the driver IC through the output, etc. But that is not what you asked about.