Yes, (digital) neural networks are algorithms.

You probably know that non-determinism in real-world inference comes from deliberately stochastic features like temperature, from implementation choices like distributed and parallel computation, and numerical effects like floating point precision.

The fact that a neural network's execution can be nondeterministic doesn't mean that the network stops being an algorithm.

The point you're making boils down to speculation that the accidental non-determinism involved in real-world inference is significant enough to undermine or negate interpretability findings based on the algorithms. That would need to be demonstrated.

The CGoL and BB examples demonstrate what might be possible in a worst-case scenario, but they're only analogies in this context. It's far from clear that real models suffer from such effects to a significant degree. You might actually be better off talking about the butterfly effect!