In mathematical modeling, “not random” is the part of the model (not reality!) that is not modeled as a random variable. This often includes theory, structure, and other other equation or dependency relationships between random variables.
In common usage, “not-random” is the predictable observations we see, the things that fit what we expect. Earlier, when I was pointing to the dirac distribution, I was pointing out that even fixed quantities can sometime be modeled as “random,” but I also noted that this is a boundary/degenerate case. That boundary does not match reality (nothing is that certain) or common usage of “random”.
Most real events have a degree of predictability (order) and degree of variation or surprise (uncertainty). The more uncertain an event is, we might say (colloquially) it is more “random.” The less order, the more “random” it is. Whatever the case, identifying a pattern (order) in data does not suggest there is NO uncertainty or randomness in the data. This is also true of random variables. They all have a degree of order and a degree of uncertainty. Showing uncertainty does not mean there is no order. Showing order does not mean there is no uncertainty. The two exist together in the vast majority of cases.