I think there is possibly scope for a separate article.  For most applications of tensors to engineering (e.g., rigid body dynamics and stress analysis), it is not necessary to accommodate the general coordinate systems of tensor calculus.  Usually there is some fixed background frame and at worst one needs to know how things transform when that frame is rotated.  Then raising and lowering of indices is also not required, and all of the tensoriality is essentially quite trivial (so suitable for engineers).  It seems to me that this is the intended scope of the article, but it might be helpful if it stated this plainly somewhere, although it is possible that I might have misunderstood what is meant by "rectangular coordinate system".

But assuming that the tensoriality of things is supposed to be trivial here, then the article should not dwell too much on this aspect of things (as it presently does).  The likely audience of the article will only get confused by this, and those looking for a more comprehensive treatment of tensors have other articles to select from.  I think some time should be devoted to discussing examples.  A good one is the inertia tensor and Sylvester's law, in my opinion, because it's very easy to visualize (for instance, in terms of a spinning plate or something).