DirectX is Windows only indeed, Linux games uses OpenGL.
But there isn't necessarily a difference in performance except for ported games (i.e. games that weren't developed for Linux, but ported after release by companies like Feral, which includes games like CoH2, F1, XCOM etc.).
Source engine based games work very well (CS:GO, TF2, L4D2, DoI etc.), Unreal engine based games should be fine too, as do many games that were right from the beginning developed to support all platforms (games from Paradox, many indie games)
Wine games can be quite difficult to setup, but luckily the Wine App database has valuable information. Some games even work basically out of the box without much user intervention (example: No Man's Sky).
It's worth a try at least for your favourite games, dual booting is annoying...