I don't think he's living on his own planet, he's actually right - jQuery runs the client side web. Not for everyone but easily 90% of sites (that actually have javascript functionality at all) will use jQuery
Rather, the practice of providing a DOM API compatibility layer runs the web, jQuery being the most widely used library of this sort. When you step out of the god-object API jQuery provides and look at the internals, jQuery, MooTools, and Closure look surprisingly similar. I find the latter to provide the best compatibility (so does Google), but that is another discussion altogether.
Your opinions on what JavaScript libraries provide "the best compatibility" has little bearing on your original statement, that jQuery is not as popular as it actually is.