First off, big O notation wasn't created with complexity theory or algorithms in mind. If I recall correctly, it has its roots in complex analysis. The notation was later borrowed as computational complexity was formalized. What happened is that people needed a way to describe the hardness or "logical sophistication" of problems and tasks. Looking into the asymptotic behavior of a complexity measure was just one means that they used. There are plenty of other ways to do this. The article reads like big O exists for the purpose of complexity analysis of algorithms. I doubt the author intended this, but they should be a bit more careful.
Time and space aren't the only resources of interest. Sometimes you need to quantify how much information you have or how much entropy there is. If you want to understand "what is basically happening", this is something you should pay attention to. Are we handling more information than we have to? What do we need and not need? Circuit sizes, sophistication of proofs, setups of databases, and the complexity of communications/protocols also play a role.
Even ignoring all this, the article is missing an elementary half of the picture: the structure of the input. It's not just about code and its design. Data structures matter, too. How information is organized, how it is encoded, and how it can be manipulated (computed on) makes an absolute huge difference. Are things sorted or unsorted? What kind of list or tree structure is your code working with? From what I understand, this is the whole point of a significant chunk of the interview questions candidates are presented with. It's ridiculous to omit this when introducing algorithmic complexity.
The author claims that Big O notation is an "awesome, not-boring kind of math where you get to wave your hands through the details and just focus on what's basically happening". They are hand waving not just the math, but also hand waving (and ignoring) most of the context as well. It doesn't even directly explain why big O notation models code efficiency in a fruitful way. It just mentions run time and memory usage superficially. In my opinion, this needs to be significantly revised or rewritten.