They don’t measure emission but body absorption. Body limit is 2 W/kg, limbs limit is 4 W/kg. Apparently only the latter limit is violated.
For meat sacks like us it primarily translates to heat. At frequencies used, this radiation can nudge molecules a bit, which directly translates to heating up. If it was in a hundreds of watts, we’d be approaching microwave ovens territory.
The limits are there because there’s a limit to how much heat a body can efficiently dissipate, and quite a few sources of it. There’s also a concern that localized RF heating can cause cancer, which is not empirically confirmed. I personally care more about a confirmed issue of the nuclear ball in the sky causing one.