Just nitpicking, but there is a biological definition of race (albeit informal), which you quote the definition of. it’s just that it cant be applied to humans because (as your quote mentions) there tends to be greater variation from within human “races” than there is between some “races”.
There’s also the issue that there’s no “boundary” or distinction between the human “races”, and an actual race would need to be distinct from the rest of the specie population in order to be recognized as an actual race.