So, I have been professional staff at two different major universities in the past.
It's easy to point at certain areas of staff growth as excessive (cue someone quoting the number of "diversity" administrators at college X) and I agree there's plenty of areas of waste.
However, the big picture is that I think the "big research university" has defined it's mission as something which is inherently going to be an extraordinarily complicated enterprise to run.
And other trends outside their control have contributed as well.
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If you think about the "research" side, most are attempting to run cutting edge labs in basically every domain, at once. That's very difficult to support from a facilities, technology, etc perspective. You wind up with numerous small groups with complex, completely different needs and few economies of scale, unlike running say, a huge R&D lab in one domain/small set of domains like pharma or semiconductors or something.
Reduced direct state funding means that universities are ever more dependent on alumni support, grant money, other fundraising, and monetization of R&D development (patents/IP). All of which require a sizeable quantity of people to oversee who do not teach or research. It is, or should be a net positive in terms of finances if you're doing it, but it certainly doesn't make stats like employee ratios look better.
On the student side, the growth in fancy student housing/services is well-covered ground I won't repeat, but is also a contributor to costs.
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The article mentions outsourcing, but fails to mention that most functions typically have reasons why they're difficult to outsource. That's not to say that none can be done, but "it's not that easy" is also true.
They mention security as an example.
Most campuses have full police departments with sworn officers, empowered to make arrests, file criminal charges, carry firearms, and so on. They can't hire an outside company to do it in their place, and given the size disparity with the towns they often exist in, local police would be unable to provide a sufficient level of service. (Nor would local taxpayers be accepting of funding it to support an entity not paying property taxes).
For public universities, this is also often a matter of state law. Ex: The NY State University Police is a state agency that handles policing at SUNY schools. No SUNY campus head, or even the head of the SUNY system, has any power to outsource that function.
There's also a not invalid perception of a different level of professionalism (even with issues with American policing) and level of required training between "private security" and "actual police officers" in most places.