Several comments seem confused about this point: the article is not about manual SIMD, which of course C is perfectly capable of with intrinsics. It's discussing problems in compiling architecture-independent code to SIMD instructions, which in practice C compilers very often fail to do (so, exp having scalar hardware support may force other arithmetic not to be vectorized). An alternative mentioned is array programming, where operations are run one at a time on all the data; these languages serve as a proof of concept that useful programs can be run in a way that uses SIMD nearly all the time it's applicable, but at the cost of having to write every intermediate result to memory. So the hope is that "more fluent methods for compilation" can generate SIMD code without losing the advantages of scalar compilation.
As an array implementer I've thought about the issue a lot and have been meaning to write a full page on it. For now I have some comments at https://mlochbaum.github.io/BQN/implementation/versusc.html#... and the last paragraph of https://mlochbaum.github.io/BQN/implementation/compile/intro....