Agree, the quote lumping the models of computation together is very misleading. Turing’s machines are immediately obvious how to mechanize and automate, even with very old technology. That was the key difference. Then proving them equivalent to mu-recursive functions and lambda calculus showed that these models of computation actually deserved to be called such. It proved that they could be implemented on a machine with no human ingenuity or creativity required to carry out the steps, which is the heart of what it means to be computable.