It's definitely more complicated than the post implies, and it most definitely is NOT only for startups. Soon after I started out - at a mature company already making plenty of money - I was a full-stack engineer. There were a number of reasons:
- New development happened sporadically; day-to-day work was a mixture of maintenance development and admin work
- Culture. They started with a small team, and never grew it. Having more people didn't fit with the way the company saw itself.
- Difficulty hiring specialists. Various reasons for it, but still valid.
At another company I worked, there was a lot of "integration development", where your time was spent connecting various internal and external systems together, software-wise, developing tools that support systems work (i.e., tools for sysadmins), and developing other tools that are for end-users, but have a heavy systems component (management software for DNS, for example.) That meant understanding each part of the stack from both a development and system perspective. Another is interest level. A few of us were full-stack developers because we were studied more than just development in our free time, and we took that with us to work. This wound up benefiting everyone. This also led to us being the go-to people (that is, the top level of internal support) for both more specialist internal developers and sysadmins, as we had deep knowledge of the internal systems from the bottom to the top the stack, and the knowledge and experience to explain and troubleshoot problems to people in those other roles.
The author is correct in that this may be more /common/ at startups (the previous startup I worked at did in fact operate as the post describes), and is sometimes done out of necessity. It is by no means limited to those environments, however.
Edit: I'd also separate DevOps from full-stack engineer. They sound like the same thing, and if you squint from far enough away, they look like the same thing. The terminology may be fluid, but I think (as some other comments state), that DevOps is more centered around "coding for systems automation", whereas "full-stack engineering" is a much more general term which can encompass a variety of different types of tasks in different environments with varying levels of knowledge/experience in the different parts of the stack/tools.