I am curious in which way programming languages with arrays are not equivalent to a Turing Machine model. It's not clear to me what you mean with "resembles" and why that would be the same thing as "founded upon".
All Turing-complete programming languages/models of computation can simulate each other with polynomial overhead. What I think is weird is that the article specifically mentions that programming languages are built on single tape Turing machines (as opposed to Turing machines in general, or random access machines), because single tape Turing machines are highly impractical and programming them would feel completely different than programming with any real programming language. For example as basic operation as array access takes a linear number of operations in the size of the array in the single tape model.