This may indeed be a very useful guide to tensors, perhaps for people who have worked with them without a strong background understanding.
I don't want to detract from that, or from the author's thorough and sincere effort to provide tutelage to the world at large, for free, in a wide variety of mathematical subjects; he seems to have written hundreds of blog posts like this one.
However, I don't think that it is in any way about conquering any such thing as 'Tensorphobia', and if it was intended to be "significantly friendly so as not to make anybody run in fear," this effort is going to fail. I do not think that it was; I think there is an (quite innocent) dishonesty to the claim, and I feel like calling this out.
The language used contains typical signals of the sort of para-academic elitism parodied in 'Fraiser', starting with the use of the uncommon word 'jest' in the first full sentence and continuing with the adoption of "we" and the scattering of various tofferies throughout remainder of the text.
I was quite annoyed by this until I looked at the author's bio page, whereupon I thought, okay, perhaps for him this feels like his natural voice. Making the grade is one of his things, and he has in fact made the grade repeatedly and excessively, and he is young enough that there hasn’t really been much time for him to reflect on this much.
He's enthusiastic about teaching, which is a rare gem of a quality amongst the professoriate. So do not be crabby, you old substandard goat, who can barely add two to two without the crutch of an operator.
Okay.
However, the author's audience is much narrower -- he is making it much narrower -- than he may realize. He is writing for a person like himself, and he is, in a somewhat standard manner, offering the subject by way of little tests of the intellect, couched in suggestions of superiority.
This is wonderful fare for a student who's sense of self-worth is founded on the suggestion that they are more clever than the others; it is neither food nor balm for the rest of the anyones who might have cause or need to seek a more general understanding of tensors.
What I take exception to is that presenting the subject in this style while claiming to speak to the rest of the anyones will tend to reaffirm 'tensorphobia' for such people, essentially gaslighting them; this is not helpful. It is a distinct harm.
I remember realizing, in my first year of university, that a person of ‘general’ (low) intelligence would in fact be entirely capable of understanding the proof of the derivative, if it was taught to them properly. Everyone routinely understands more complicated things. The true barrier would be their indifference; they would have no use for such understanding. But otherwise the failure would not be on the part of the student; it would be on the part of the teacher.
I am not suggesting the same of tensors; perhaps I myself lack some quality that is needed to understand them. But I recognize the language that is being used here, and it has an easily comprehensible and distinct meaning that has nothing to do with tensors.
I think the author is doing wonderful and useful work, but I think he should reflect long and hard on his rhetorical affectations.