It's not because of the volume (capacity) of headspace. Headspace is similar for a keg as it is for the same volume of beer in bottles. Someone on here years ago did some measurements of each and found that the headspace in a keg is actually slightly higher. I think (just guessing) it's a combination of two things to do with headspace though:
1. Most brewers, after filling the keg, purge then pressurise the headspace in the keg, thus it's already full of pressurised CO2.
2. When you open a bottle, you lose the pressure from the headspace; this equivalent pressure/CO2 is never lost from a keg.
When I keg primed (I mostly spund now), I used about 2/3 of the sugar that was needed for the same volume in bottles.