Sounds way too complicated ...
Sometimes, life is complicated.
Each time the gate is charged or discharged, an amount of energy equal to the gate energy is dissipated in the gate resistor. From this energy, and the switching frequency, you get a power.
Let's take a really crude approximation to get into a reasonable ballpark. If you had an equivalent gate capacity of 2 nF, charging to 15 V, that's a gate energy of 225 nJ. With 100 kHz switching, that is being dissipated 200k times per second, or an average power of 45 mW.
The word 'equivalent' is doing a lot of heavy lifting there. If you want an exact gate energy, then you'll need to integrate the gate charge/voltage curve for a particular drain load. But you'll often find that a back of the envelope approximation will show you're well within dissipation limits for standard components.