The middle east is referred to as western Asia. Because it is in western Asia. People who come from Asian countries are referred to as Asians.
I do get your point however, as it makes them sound like they’re Chinese or something to us Americans. The Brits know exactly what they mean by Asians.
“Asian” is this context is Media-Speak, designed to muddy the waters. No one in Britain (apart from the brainwashed/brainwashing PC) refers to Iraq, Syria or Bahrain as “Western Asia”. They are Arabic nations in the Middle East.