As marriages are (generally) not arranged in this country, all marriages are about personal preferences. Mildred Loving, a black woman, chose a white man to marry. She was as free to marry a black man as any gay person is free to marry a straight person of the opposite sex. The case is completely relevant, and saying that "race is not a choice" is immaterial to the matter; the trial was not about race, it was about the freedom to marry the person of one's choosing.

No, Loving v. Virginia is not just specifically about race. It recognizes marriage as one of the fundamental rights.