> "Non-determinism" (i.e. the "N" in NP-Complete) does not mean "random", it means "following all paths at once" (there's a really elegant way to understand the List monad as representing non-deterministic computing). It's such a fundamental (and delightful) concept in computer science that refusing to understand what it means is a tragedy related to the loss of technical language itself.
You opened by expressing disdain for articles that misuse the term "non-determinism", then proceeded to give a definition that also misuses the term "non-determinism" in the given context, or at best is a bit too vague for anyone to gain insight from.
Here's a better definition:
An algorithm that can produce different outcomes, for the same input, on different executions.