Why did it become so much more expensive to start a university?

Besides all the factors that the other answer already lists, the elephant in the room is that KAUST has explicitly been designed to be a world-class university (rather than organically growing into one, as was the case with your other examples).

In short, it is not so much more expensive nowadays to found just any university - in fact new universities get founded all the time, virtually always spending considerable less money than $10 billion - but founding a university with the expectation that it will compete with the best in the world in a very short time frame is expensive. You need to compensate for all the natural growth in budget and prestige that established universities had over the last one or two centuries.

I would add two other factors to the good answers already available.

1. Growth of science into multiple fields and disciplines have resulted in increased costs. Back in the day, for example, mathematics was considered one field. But nowadays, there are many diverse subfields within mathematics (e.g., pure maths, statistics, computational math, etc). Creating a university with various departments and faculties results in more human resources cost as well as facilities and equipment costs.
2. To make scientific and technological advances possible, research has become more relient on expensive lab equipment in the late 20th century and 21st century in comparison with the early 20th century and before that.

I suspect that you’d probably need to look at the budgets for the institutions in question to get a definitive answer, but I can think of a few potential causes:

1. Increased administrative and bureaucratic costs. In the days when those universities opened, HR departments weren’t a thing, and there was significantly less regulation on businesses in general.

2. Increased cost and quality of facilities. Technology marches on - and the cost of building a university building before indoor plumbing was a thing is radically different to building a modern university building with electricity, running water, IT infrastructure, projectors and cameras for the lecture theatres, and all the inspections and certifications being done to make sure that all the work is being done in accordance with code.

3. Computers, in general. That’s an entire field of costs that didn’t exist back then - not only do they need the physical infrastructure and desktop computers for the staff and students to use, but they also need to pay for licenses for all the software that the students would use for their classes, for the university website, for their online learning system, for their class and room allocation system, for their centralised marking and enrolment system, etc.