SLAC National Accelerator, a National Lab that Stanford happens to run, employs about 1,600 people. They don't necessarily need to interact with students; other national labs are run by corporations (e.g., Sandia is run by Honeywell).
Stanford has a massive medical system, including an adult and children's hospital. They are teaching hospitals, and so part of the point is to train medical students and residents, but they also need all the staff of a regular (actually, top-of-the-line) hospital: doctors, nurses, techs, porters, billing, payroll, etc.
On top of that, Stanford also has a massive research program funded by grants from (e.g.,) the NIH, NSF, and DOD This requires people to actually do the research (heavily-funded profs rarely teach, plus postdocs and research scientists) and support it (animal health techs, machinists, etc). There is also a lot of bureaucracy involved in getting, doing, and accounting for that work. It certainly depends—in part—on grad student labor, but it's also not directly linked.
> "The campus provides workspace for about 2,700 employees (including three of the university’s eight vice presidents) working in critical areas such as the School of Medicine administration, libraries and archives, business affairs, human resources, development and Land, Buildings & Real Estate. Stanford will be the city’s third-largest employer in Redwood City."
Administration for the school of medicine is literally the first group cited.
Stanford Medical is everywhere around here.
The rest of it takes administration. The folks at SLAC need to get paid. Someone needs to check that the doctors and nurses at Stanford Medical are appropriately licensed; once they are, someone also needs to find somewhere for them to park.
They list what's out there: https://redwoodcity.stanford.edu/about/campus-directory, which also includes Stanford University Press and the Tech Transfer Office.