“a political philosophy, movement, or regime (such as that of the Fascisti) that exalts nation and often race above the individual and that stands for a centralized autocratic government headed by a dictatorial leader, severe economic and social regimentation, and forcible suppression of opposition”

Genocide is almost always committed by fascist regimes, but in and of itself it is unrelated to the political system/philosophy. You could theoretically have a perfect democracy where the people vote to genocide another culture and it would not suddenly make their political system fascistic.