Yeah I guess "classical" can mean different things depending on the context.

Great post! Planning to publish this?

In statistics jargon, classical methods are all frequentist inference methods which rely on asymptotic theory and p-values. Some of them, like linear regression, logistic regression, or ARMA models are nowadays viewed as ML. I guess the "ML" label is a bit vague and changes over time.

So what is an example of a non-statistical method?

All funny and right on the spot except the one about "proving what had already been known empirically for 5 years". That would be actually a big deal.