"That doesn't mean race doesn't exist"
Exactly, although not in the traditional sense. There are many many overlapping genetic aspects in humans; We subdivide for political or social reasons, not strictly biological ones. To make the height comparison more fair, it would be as if we divided people into "bigs" or "littles" arbitrarily and formed political parties around it, etc. Height is one biological aspect and even then what is "tall" is subjective.
For example, the US viewpoint of white or black(~=african) is a relatively recent way of looking at race. People don't slot neatly into X or Y buckets.
I recommend reading the wikipedia article on Race [0].
0: https://en.wikipedia.org/wiki/Race_(human_categorization)
