Right, you are hinting at the angle that other commenters have pointed at, which is that Vanguard runs a fund management business (which is what the article is

Right, you are hinting at the angle that other commenters have pointed at, which is that Vanguard runs a fund management business (which is what the article is about) but also runs a brokerage, does 401k/403b/529 administration, has an advisory business, etc. The total employee count refers to employees working across all those business units, and that includes a lot of customer service, regulatory, back office, etc.