Alikhalid--whether we like it or not Arabs do 'believe in a country called Israel'. Or at least some do. Hence plenty of nations in the regions, rightly or wrongly, recognize it as a nation and sign treaties with it.
But from what you wrote, it seems you would consider it part of the Arab world, but a part occupied and run by usurpers. So would you consider Iran part of the Arab world? You don't list it, but on you definition it sort of fits, but sort of doesn't. Personally, I would say no, on the same grounds I would not include Turkey. But then I would hesitate to include much of North Africa.