take into consideration MOSFET avalanche parameters and include them into the overall average power value?
That particular image is for a resistor not MOSFET.
LTspice doesn't inherently know anything about avalanche effects. That must be built into the MOSFET model, which may be provided by a third party. I would guess that most MOSFET models do not include this behavior, but as @the-photon suggests you can run a simulation to determine that yourself.
LT spice is simply taking the waveform over the given amount of time and summing up all of the values. The thing to remember is the waveform is sampled and not continuous (as in continuous functions). That means if the simulation has effects that are smaller than the timescale they will not be integrated, so set the simulation time-step appropriately. It also means Nyqusit sampling applies.
Another thing to keep in mind is LT spice has variable and fixed solvers, the variable time step solvers are mostly good at simulating high resolution\frequency simulations but sometimes have difficulty. Neither solver will simulate a time step beyond the maximum timestep specified in the