Yeah they use the term asian there to cover middle eastern people too...
That's because the whole of the Middle East is in fact a part of the Asian continent. Look at a map of the continents. This comes up every other day here, it seems. I'm surprized some long time posters are still puzzled by this (the poster you responded to, not you).
So the Brits use a designation based on continents, not 'regions'. Big deal.