I don't think there's anything necessarily wrong with the term "user." It's a top-level generic term that could be broken down to better describe those who use your service. In Square's case, that's "buyers" and "sellers" who are both "customers" of the Square platform.

It seems obvious, but I understand what Dorsey's getting at. I've struggled with finding appropriately specific identifiers, and when in doubt just lumped everyone together as "users."

Context matters. Square happens to be one of those paid services whose categories of "users" are pretty easy to identify and name. Like you guys mentioned in your comments, redefining specific terms for "users" of free services and search engines isn't quite as simple. I would suggest "freeloaders" or "browsers" but that would take us in the wrong direction :)

I'm content being labeled a "user" for now.