I don't think I agree with you, Mr.X.
"Japanese" is a proper adjective. And I don't know what you read in the Oxford guide, but I fear you misinterpreted things:
"4. (often initial capital letter) of, pertaining to, living in, or characteristic of the West, esp. the western U.S.: a Western ranch.
5. (usually initial capital letter) Occidental: to adopt Western dress.
6. (usually initial capital letter) of or pertaining to the non-Communist countries of Europe and the Americas: Western trade agreements." - Random House
This is a question I often wonder about too. The CED gives western as an adjective and there is no capital. Yet, couldn't we say that when Western is intended to convey the idea of 'belonging to Western countries' (namely a sort of identification, if not of nationality, at least of a group of cultures or countries as opposed to Asian countries for instance), then the capital W could be used?
As we're on a sphere, most things are westwards of other things. So you can have food from western places.
I see "Western food," in this context, as a rather specific category given as a contrast to Japanese food.
It's a rather fuzzy distinction, I suppose. The CED link also gives an example of "Western" as a proper adjective.