If your table is furry and has a tail it may actually be a cat (from a machine learning perspective).

The machine learning packages have an einsum function / tensor contraction, etc. What more do you need for it to be called a tensor?

I'm not familiar with tensor contraction as practiced by a machine learning package, but summation convention is just that, it's not a fundamental property of tensors.

As a way of describing physics or geometry they have additional structure which I'm not seeing.