Honestly I'm learning every single day for 6 years, but there are a bunch of words I simply don't know and a bunch of abstractions I don't understand the need described in this article. The future (maybe even the present) looks unnecessary complex to me.
The "old" way still works, and won't stop doing so. If your deployment needs are not too fancy, these are still easier to reason with and maintain, too. e.g. a one-man operation who manages a handful of mom-and-pop businesses' websites, it makes no sense to go too fancy. A simple git clone on a simple LAMP setup, or hell, a shared host through FTP, works just fine.
Introducing these things prematurely are just asking for trouble. They come with their share of complexity and overhead. However they do solve some problems. In a lot of cases, if you don't know about these things yet, you probably don't need to.