PRNG = Pseudo-Random Number Generator

Computer based random number generators are actually pseudo-random. They are not truly random but the result of a mathematical process to generate a series of numbers which can “pass” for random while being the result of a deterministic computer algorithm.

The “direct” part isn’t part of the math. I believe that refers to using PRNGs all with the same seed value or with a known and possibly poorly developed randomness algorithm.

The vast majority of random number generators used in slot machines are PRNGs. The reason “real” RNGs aren’t used is they are very difficult to achieve. Real randomness is quite difficult to prove as well. Most scientific/statistical testing use PRNGs. As long as the limitation of the particular PRNG is known, there is no reason not to use it. ‘True’ RNGs generally use natural phenomena to produce randomness, like the result of radioactive decay or thermal noise or some kind of quantum effect.

Examples where PRNGs breaks down: using a PRNG that repeats every 2 million results to produce 10 million results. Using a PRNG algorithm with a known algorithmic flaw. Using a PRNG on a CPU with a design flaw that breaks the randomness.

For slot machines, the problem isn’t with using PRNGs. They are widely used around the world, after all. The problem is with using them poorly. Slot machines aren’t built so shoddily that you can get at the coins inside easily (back in the days they still had coins). Likewise, the PRNGs used in them shouldn’t be so shoddy they can be abused.

ETA: classic slot machines had a similar issue with repeats. If a machine was poorly designed, the same results would show up with some frequency. You could abuse that by ‘camping’ by a slot machine until you knew it would pay out. A designer can get around that by making the repeating pattern very large (like 100000 spins) before a pattern repeated, but the easier solution is computerization and PRNGs (and re-seeding them periodically).