Bio-Form. ICRPG (Index Card RPG, 2d Ed.). ICRPG has medieval fantasy, sci fi, and gunslinger campaign settings but can work with pretty much any genre.
Description / Adjectives / Talent / Abilities. Some games, like InSPECTREs and Paranoia do not have anywhere on the character sheet to define "race". Perhaps because everyone is typically human, but you can play bots in Paranoia and in InSPECTREs you play supernatural or other non-human characters. In games like this you just describe your character however you want plus give some adjectives or talents that may have mechanical effects. One problem with InSPECTREs, however, is if you are non-human, you don't get a talent. Instead, you get "Weird Abilities." That may be problematic, except that it is trying to capture a humorous, Ghostbusters feel.
Origin. The Expanse RPG. Again, you are generally playing one of three "kinds" of human: those from Earth, those from Mars, and those from "the Belt." But the concept can work with aliens just as well, IMO.
Peoples. Carnival Row, based on the TV series, using the Cypher system.
Kin. Labyrinth Adventure Game(based on the Jim Henson movie of the same name)
Race, but non-human genders ignored. Empire of the Petal Throne uses the term "race", and it describes human societies where women are typically subservient, but creates a legal category where a woman would be treated same as a man. Seems fairly progressive for a campaign that came our in 1975. What I found interesting, and has forgot about, is that gender was ignored for non-humans, as the concept was just too different from human conceptions to matter for gaming purposes:
Noun. In No Thank You Evil! A Genre-bending RPG for kids based on the Cypher system, every character is defined by up to three elements that make up a colorful description—they form a sentence you can say: I’m a [adjective] [noun] who [verbs]. E.g., I’m a Fast Superhero who Experiments with Science; I’m a Kind Prince who Reads Great Books; I’m a Powerful Robot who Flies through the Sky.
Draw a Picture. Hero Kids is a fantasy RPG designed for children. You draw a picture of your character, which can be anything. Then select attributes, attacks, and skills that make sense for your character concept. E.g.: