I've only played D&D for a couple years and don't have extensive experience with githyanki lore but my impression is they're not so much bent on genociding other races as they are exterminating the mind-flayers that enslaved, tortured, and fed on them. Everything about the structure of their society and their philosophy on the value of life hinges around that. They became hyper militaristic - only the strongest and most capable are valued. They seem to regard other races as largely weaker or simply unworthy/uninteresting, but aren't looking to kill or subjugate them, they're just irrelevant.

I'm only ~near the end of Act 2, but Laezel's development has been some of my favorite stuff about the second act.