I can see how the twin aperture factors in that equation. Not many existing AAMs are armoured enough anyway, and I'm not sure if the boundary air surrounding an AMRAAM is hot enough to render even a measly 50kw laser useless, especially when the missile is in its last-mile cruise phase and slowing down.
It seems extremely doubtful those apertures support any kind of DEW. A laser would not use a large sensor window; it would use a trainable mirror. And if the goal was shooting down missiles, then only arming along the frontal arc shows a lot of faith in the system and the pilots - since they would not be able expose their tail in a fight.