Ignoring that you are making an assumption about how the randomness is handled, this is a very vacuous definition of "deterministic" in the context of the discussion here, which is AI controlling large and complex systems. The fact that each inference can be repeated if and only if you know and control the seed and it is implemented with a simple PRNG is much less important to the conversation than its high level behavior, which is nondeterministic in this application.

If your system is only deterministic if it processes its huge web of interconnected agentic prompts in exactly the same order, then its behavior is not deterministic in any sense that could ever be important in the context of predictable and repeatable system behavior. If I ask you whether it will handle the same task the same exact way, and its handling of it involves lots of concurrent calls that are never guaranteed to be ordered the same way, then you can't answer "yes".