That's because flexbox is still prefixed in Safari 8 (see http://caniuse.com/#feat=flexbox). Just add -webkit- versions of all of the properties as well and it will probably work. e.g. "display: -webkit-flex".
Yes, pretty disappointing that a tutorial on flexbox fails to prefix its styling rules - which in this case is very much essential to make your point.
Since I use autoprefixer in all my projects and only need to cover moderately modern and relevant browsers, flexbox has been a regular companion for me - without any problems. So many layout headaches that can be avoided with this great addition to CSS.
Here's how the site looks for me in Safari 8.0.8: http://imgur.com/aYwYTDx
Safari seems to refuse reading flex style: http://imgur.com/LEhtYBZ