Caniuse says that IE11 has a lot of bugs regarding flexbox. Firefox supports flexbox only since 2013-2014. So it would make sense to add a simple non-responsive fallback for older browsers.
Also, if I remember correctly, the default browser in Windows 7 is IE9. It makes sense to support default browser in the most popular desktop OS.
Some of older browsers, released in 2012-2014 support flexbox only with vendor prefixes, but the article doesn't has rules with prefix. As frontend devs tend to copy the code without much thinking, we cannot expect that they will add the prefixes or fallback code themselves. So it will be author's responsibility for web sites being less accessible in different browsers.
caniuse.com also has the combined global market share of IE 6-10 as being only 0.46%, which is completely insignificant for most websites. And I've personally been using flexbox on IE 11 for years with very few issues.
> Some of older browsers, released in 2012-2014 support flexbox only with vendor prefixes
Again, these browsers represent a tiny fraction of the total market. Firefox and Chrome auto-update by default, so there is no reason that someone should be on a version from 2012.
These days it simply doesn't make sense to have a fallback for flexbox unless you're specifically targeting older versions of IE. (And even then, I've had some luck getting flexbox layouts to work on IE 10, even though it's more effort.)
Global market share stats are applicable for global target websites. Consider any medical equipment company for example - their clients will browse the catalog from archaic, unmaintained PCs they have laying around.
Always get data about browser market share from your client if they have it, otherwise you're simply in for an uncomfortable surprise one stats start coming in.
HTML/CSS was designed to be forward/backward compatible and not to be written only for version of Safari installed on dev's macbook. This is against the spirit of HTML.
If I understand right, you are suggesting it is "against the spirit of HTML" to write CSS that isn't backwards compatible... infinitely? You have to draw the line somewhere, right? An ancient enough browser won't support CSS at all. Using only CSS that would be supported by a, say, year 2005 browser would also be pretty limiting.
You can choose to do that if you want, but I think your opinion about the "spirit" is a minority one.
I haven't had any trouble doing flexbox for IE11. I always make sure to test in IE11 because of the caniuse warnings; I have very rarely run into any problem with IE11, maybe once or twice, and they were easy to work around problems.
I wouldn't be scared of using flexbox even if you need to support IE11. I'm not sure where caniuse's dire warnings come from. (I have run into different flexbox behavior between FF/Chrome about as often I have run into flexbox problems with IE11; I generally couldn't tell you which of FF or Chrome is correct/incorrect in those cases).
I've in the past done flexbox without too much trouble even on IE10, but I am not myself concerned with IE10 anymore.