Even when limited to the Subcontinent, "Asian" is hardly a racial term. There are dozens of races in the region--Tamils, Nagas, Punjabis, Sherpas, etc. Winston Churchill once commented that making India into a nation-state would be like turning the equator into a nation-state.
Indeed, though the same applies to the US use of ‘Asian’ - there are many races between Mongolia and Indonesia!