EIRP adjusts the total radiated power for the antenna gain.
So if you're transmitting 1 W and your antenna has a gain of 30 dBi (1000x), that's equivalent (from the perspective of whatever it's pointed at) to an isotropic antenna (no gain) emitting 1000 W at the same distance.
It should be obvious that EIRP is what matters for interference and human safety, hence why the FCC regulates EIRP instead of power output.
So if you're transmitting 1 W and your antenna has a gain of 30 dBi (1000x), that's equivalent (from the perspective of whatever it's pointed at) to an isotropic antenna (no gain) emitting 1000 W at the same distance.
It should be obvious that EIRP is what matters for interference and human safety, hence why the FCC regulates EIRP instead of power output.