He's saying process mining is machine learning in a colloquial sense; something (insights) are being learned from data with a machine. You are right that this isn't the proper scientific definition, which is that an algorithm is learned from data.

It depends on how you define machine learning. Using process discovery, you learn a process model (for example, a Petri net). Such a model can be seen as a function describing a possibly infinite set of process executions (also involving concurrency). One can see this as a classifier for behavior, just like a neural network distinguishes between dog and cat pictures. Process mining is also used to predict the remaining processing time of running cases, predict bottlenecks, predict deviations, etc. There is more to ML/AI/DS than just neural networks and gradient descent and also these techniques use a fixed algorithm :-)

It is called mining because it is not just about process analysis but instead about mining these hidden processes from event data.

That’s the point. You have to tailor the skill to your use case. It’s like doing a study to break down all the interactions and plug in solutions ad-hoc