How does that use the diagonal argument? If the diagonal argument could be used it would be to prove that the number of submarine routes isn't countable.

Edit: just looked at the SVG called "Diagonal Argument.svg". That's not what I know as the diagonal argument (https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument, http://mathworld.wolfram.com/CantorDiagonalMethod.html)