The question referred to is here
The OP asked for:
Were there other related definitions defined around this time?
How has today's definition of a tensor changed compared to its beginnings?
My focus was on the latter.
The question was deleted by a moderator, who at the same time, explained why I was wrong - he commented:
"Here you are describing only a certain type of contravariant 2-tensor, known as a 2-vector (these lie in ⋀2(TM)⊂⨂2TM, not an arbitrary contravariant 2-tensor."
This is quite wrong and he betrayed his own knowledge of the subject by stating that I was describing an contravariant antisymmetric 2-tensor field when in fact I was discussing - as the OP requested - the modern notion of a tensor.
Whilst the moderator acknowledges that I mention some history in the subject - I mention that Einsten & Infeld explore the subject of a vector; I think its safe to say that they didn't feel the notion of a tensor field could be easily explained to a lay public; I've read enough around the subject to know that there is No book on the subject - it is yet to be written.
Given all this, I'm asking the moderating team to reinstate my post.
I rewrote my post to include an explanation as to add more detail to my discussion of what a tensor is (and which shows, despite @danu's accusation, I wasn't discussing a differential form, but the modern notion of a tensor defined by universal properties). This was deleted by a second moderator (@HDE226868)...his reason - those given by the first moderator (@Danu)...