RF Output Power vs Antenna gain
An isotropic antenna would emit power in all directions and have 0 dBi gain (The "i" stands for "relative to isotropic").

Your whip antenna is omnidirectional but not isotropic. It emits power equally in all horizontal directions: north, south, east, and west; but it doesn't emit much power straight up into the air or down into the ground.  It has 2 dBi gain because by not emitting up and down, it can send more power horizontally. But no receiver will receive even close to 1 W from your transmitter unless it completely surrounds you in all directions.

A more directional antenna, like a horn antenna, will only emit in roughly one direction, for example, north.


(image source)

This antenna will have higher gain than your whip, 13 dBi according to the designer, but still no receiver will get more than 1 W from it. They'll just get 13 dB more than they might have got from an isotropic antenna that spread the 1 W over all directions. And of course if they stand off to the side or behind the horn they'll receive much less power than they would have from the omnidirectional whip antenna.