Does that actually require unpredictability? Or is it just a defense in depth type thing where we believe we don't need it, but some unknown vulnerability/attack might make unpredictability beneficial?
Sibling comments are completely correct. Graphics simulations often require quasirandom sequences; the particular sequence is not important, but any correlations in the sequence will be visible in the output as artifacts, so we want a decorrelated sequence.
If this is not enough of a real-world example for you, then Monte Carlo methods also show up in weather modeling, financial planning, and election forecasting. In those predictive systems, there is extreme uncertainty and dependence on initial conditions, which we model with quasirandom sequences and seed numbers respectively. By running many simulations with different random sequences and then examining all of the results statistically, we can get good estimates of future behavior.
Edit: Oh, you're not in good faith. Okay, cool story. Best of luck with whatever imaginary idea of "unpredictability" you're trying to define, but you might want to return to actual maths at some point.
Every other thing in the PCG website and in this thread attempts to be similar to random (with varying degrees of success). No one here is trying to intentionally be different from random.
> Sibling comments are completely correct.
No sibling comment says anything about quasirandom. The sibiling comment mentioning graphics (by Karliss) actually sort of disagrees with you, and says that we want stuff to be as close to random as possible for graphics so that players don't see patterns. Of course there can be multiple types of graphics situations, some where quasirandom would be useful (the blog you linked), some where a real random approximation would be useful (Karliss's situation).
> Wouldn't the second category be more less CSPRNG?
The website says PCG is "Challenging" to predict and ChaCha20 is "Secure". So I think this means that PCG isn't a CSPRNG, but still is harder to predict than Mersenne Twister.
But is this useful at all? I don't know. This thread started by andreareina asking that exact question: "What applications require unpredictability where you wouldn't go full csprng?" People immediately then misunderstood the question because they misunderstood how the word unpredictability is being used.
A player not being able to mentally predict enemies and not seeing visible patterns sounds like it might fall more under the website's definition of "Statistical Quality".