It looks like she wants to talk about symmetric monoidal categories, not just monoidal categories, for that’s where the calculus of string diagrams is actually useful.
Tensor categories is another word for symmetric monoidal categories, indeed it’s less of a mouthful, and perhaps more “intuitive” - it’s conventional to write the symmetric monoidal structure as a tensor product.
Tensor categories is another word for symmetric monoidal categories, indeed it’s less of a mouthful, and perhaps more “intuitive” - it’s conventional to write the symmetric monoidal structure as a tensor product.