- It's not as verbose
- The concept of tensor has linear algebra operations associated with it while multidimensional array is just a programming term without any attached Math operations.
But that's the precise problem. The multidimensional arrays that programmers call "tensors" do not generally have the operations defined on them that you would expect from a tensor, such as index contraction, tensor products, or differentiation. At the same time, a tensor is different from an array, just like a number is different from its decimal representation. These distinctions are important when you want to change the basis, a very useful and frequent operation for both tensors and numbers.
Then again, this battle was already fought and lost for vectors, which programmers specialised to mean "arrays" instead of meaning "elements of a linear space".
there is already well defined language for this. multidimensional array is fine, psuedotensor is fine. tensor is confusing if you have any previous background with tensor calculus before the word became machine learning flavour of the month.
still. this does look pretty cool overall. processing large volumes of data is becoming increasingly less specialised and more generic, which can only be good. :)