When I started getting in to coding and started focusing on refactoring, it amused me how close that was to the process of writing poetry (at least the way I was taught). Write it all out. Then cut some, add less, cut some more, move some things around.
I think Atwood is missing the bigger picture that both writing and programming are forms of creating. They are both textual, sure, but they fall better under this bigger umbrella of design.
So I wouldn't say coding is just writing, they just both happen to involve text.
However, every art form (by "art" I refer loosely to anything that requires practice to master) is judged based on its method of transmitting information. The Elements of Style wouldn't help a painter. It absolutely would help a programmer. It would help a screenwriter, a lyricist, a playwright.
The fact that both programming and writing deal with text mean that they have text in common. And learning how to write is something that helps you in both scenarios.
Coding IS just writing. However, it's writing with a different purpose than journalism or novel-writing or poetry. Doesn't change the fact that all of them rely on text and ONLY text as a medium.
As a single example, it is often useful to repeat a point when writing to hammer it home. Doing this in code just creates maintainability issues.
I know this wasn't the core of Jeff's point. I think his point can be more clearly stated:
It is important to be clear first and terse second when writing and coding.