Yeah, I agree that Watson’s comment is pretty much meaningless. Probably the most important factor is that over the past several centuries, “western” culture (which, let’s not forget, has been shaped with lots of input from other cultures) has increasingly become “world” culture. Particularly in science, technology, and academic/intellectual pursuits in general, the norms of the European-descended former and current political elites have become to a large extent the norms of the whole world.
It’s not too great an exaggeration to say that these days, unless you’re part of a so-called “traditional culture” (in which case your great ideas are not likely to attract much notice from the world as a whole), you’re part of a culture that is to some degree “westernized”. So all your artists, scientists, scholars, politicians, etc., might be described as working in some kind of “western tradition”. Does that mean that all their ideas are essentially “western” ideas and there are no longer any “non-western ideas of note”? That’s kind of like saying that modern astronomy is “Greek” astronomy: if you’re going to define cultural and intellectual traditions that broadly, they lose most of their useful significance.
By the way, though Gandhi trained as a barrister for a few years in England and was certainly greatly influenced by Westerners such as Tolstoy and the Theosophists (themselves strongly influenced by Hinduism, of course), the strongest single influence on his moral and social thought seems clearly to have been the Hindu religious tradition, specifically bhakti Vaisnavism.
Also by the way, I kind of question the attempts to disqualify, say, non-western medical practices on the grounds that they’ve been around for a long time. Recall that modern Western architecture, literature, art, etc., also draw on lots of ideas that are very old. Integrating a traditional art or science into modern culture, IMHO, is a legitimate candidate for a twentieth-century “idea of note”.