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That depends on your definition of "random". They're non-deterministic; the same inputs will produce multiple outputs, and I think that's the point.
So, it depends whether you're referring to most people's definition of "random" or a mathematician's, because they often differ. One characteristic of "true randomness" (as defined in mathematical terms) is that eventually, by accident, patterns emerge. When people inevitably notice these patterns, the system appears less random.
Systems that check ahead for such patterns and adjust outcomes to avoid them are called "pseudo-random". Even though the outcomes are carefully calculated, they're perceived as being more random because they lack patterns.
Notable examples I can think of off the top of my head are Diablo 3 and the official Risk mobile app.
In Diablo 3, the drop tables started off using a truly random number generator. Some players noticed long stretches of no legendary drops, other players saw multiple legendaries in a row. People complained the drops were "rigged", so Blizzard altered the algorithm to be pseudo-random and players stopped ccomplaining. Now, if a certain amount of time goes by and you haven't had a legendary drop, you're guaranteed one. Once a legendary drops, you're guaranteed NOT to have one for a certain amount of time.
With Risk, same story with the dice rolling algorithm; players abjectly refused to accept the outcomes were random, despite the devs adding functionality to count your dice rolls and every players' showed a perfectly uniform distribution.
A mathematician would agree that an LLM isn't random because the next node in the chain is determined by the current nodes. But, since the algorithm won't generate the same output every time it's provided identical input (like a calculator), that satisfies most people's definition of the word "random".