It makes sense as a universal dynamic.

When living in contact, hunter gatherers and farmers are in natural conflict since the most concentrated food source you could gather (or hunt) from is a farm. Raiding must have been fairly common.

In a conflict like this, it seems natural that the farming community would prevail, since they would naturally be more motivated to do so (this is their primary food source, they are the ones being attacked), and as a stationary community might be expected to build up more resources and be better prepared to defend themselves.

Interestingly enough, agrarian societies being invaded (and then ruled) by nomadic tribes has been a recurring phenomenon in the past two millennia (by the Arabs, the Turks, the Mongols, etc.)

And because the farming communities would simply outnumber the hunters, since they are exploiting photosynthesis more directly. A given area of land can sustain many more farmers than it can hunters.