Is 'Western Philosophy' just a misleading term for 'Philosophy'? Philosophy is located in culture, Western philosophy cannot be Philosospy because the world has only recently become such an open, easily traversed place. Global culture will spawn Global philosophy, a justification or rejection of societal rules, ideas, beliefs that span the whole world.
T claim Western Philosophy doesn't exist is to claim that the West doesn't exist. Or that mindsets and thought patterns are not different in multiple cultures. It might be a generalisation, yes. But the old thinkers that you so adore interacted with other philosophers, Italian philosophers with german philosophers and so on, the resulting back and forth of ideas and philosophies can be called Western Philosphy. Or in the East, Eastern Philosophy. I suppose Western Philosophy can also refer to what some might consider Christian-influenced Philosophy. Religion does form culture.