he's definitely doing it wrong there. As a scientific C programmer, I would never do that, I would malloc one contiguous array of nrows*ncolumns. And my freeing of the array would be as simple as his Fortran deallocate.
Sure, C could make multi-dimensional array handling nicer, but I have macros that basically do his A[x,y,z] for me, admittedly a bit more verbosely.
Many of his points about Fortran are true, but almost all his statements about C are false. Or nearly so, yes, copying an array of floats requires calling a function, memcpy, and not just using an equals sign, but that ain't rough and falls into his idea of "what actually happens ‘under the hood’ inside a computer". And others are easily handled by adopting things like the MKL (want to take the sin of everything in an array, see https://software.intel.com/en-us/mkl-developer-reference-c-t... )