Sure, but even if we continue to abide by this inconsistent terminology, "eastern Asia" is not the same thing as China, so the OP's point still seems relevant.
I'm not endorsing the use of the terminology, nor do I use it, but that has been my experience with others who use it in the US and UK. I know the US Census lumps Indians and Chinese together in one as Asian, but colloquially, I never hear anyone in the US refer to Indians as Asians.