I think you're splitting hairs here. Not sure what definition or context of determinism you are using, but in most scientific fields not only is probability the de-facto example of non-determinism, but in fact the words are often used interchangeably.
By definition, if your outcome is a random draw from a probability distribution (known or unknown), you cannot guarantee the outcome in a deterministic manner; you can only guarantee that in the limit, a large number of random draws will follow that distribution (known or unknown). But that's not what one would typically call determinism.
In formal methods, a subfield of computer science, we'd typically use the definition of non-determinism that is widely used within our own field. For example, see: https://cstheory.stackexchange.com/questions/632/what-is-the...
I don't think that link contracts anything. It just says that probability is a subset of ND but not vice versa. Which is true. But this is not the same as saying probability is not ND. Maybe I'm missing something...
Non-determinism comes from transitions which have no known distribution and might cause your program to take alternate execution paths without any predefined rule. That's clearly not true in your example.