The entire blog post is about how to over-engineer FizzBuzz for fun and learning.

Using WordPress is "over-engineering"?

Yes

WordPress should include a cache switched on by default then you have to turn it OFF as an advanced setting. That'd be good for performance and the environment :-)

But using Wordpress is no more overengineering than buying a car. (Versus building your own 2 stroke engine because it's simpler).

Wordpress is under-engineering. It's what you default to when you don't want to do any engineering and just deploy the standard blog solution that everyone's familiar with.

More or less so than running a static site generator that lives on one particular machine, and using Git to push your changes to the server?

More like use a static generator to push to S3, optionally with a Cloudfront distribution in front of it.