"riot resulting from racial hostility," by 1875, American English, from race (n.2) + riot (n.). The thing itself is older; in the Jacksonian era it was comprised in the general term mobbing.

"a race-course, the path over which a race is run," 1814, from race (n.1) + track (n.).

"relating, pertaining to, or characteristic of an ethnic race or race generally," 1862, from race (n.2) + -ial. Related: Racially.