I fully support google on this. What use is your great content if I have to pinch and zoom to actually read it ? It's not hard to make your content responsive to the viewers screen size.
There are dozens of screen configurations and at least four different browsers you need to prepare for. If it would be easy, people would do it. But when you factor in the time and effort, it's just not worth it. Unless, of course, you're a big company with hundreds of employees.
Don't forget the project management triangle. Quality, cheap and fast. Pick any two.
I'm not hostile to mobile users' needs, but I'd much rather have a mobile web of occasional pinch-to-zooming than one of annoyingly crippled large-text-fests.
Seems like this is controversial, though.
The site you mentioned probably won't be affected since you're likely not in direct serp competition with anyone else, so you can choose to ignore their advice if you want.