For game engines there is a lot of material out there explaining the basic processes and data flows; there are free or open source games and game engines around as well: Unreal engine, used in the article, is free, including full access to the source code. (This is by far the most widely used game engine in the entire gaming industry). And with a graphics debugger (free) you can look fairly easily at how games (pretty much any game you can run on your PC) render things as well.
That's not to say that game engines are simple, however, it is relatively easy to understand how they work on a basic level (i.e. what they have to accomplish and how they do so in general terms) and, specifically considering graphics, simple renderers are not particularly hard to develop yourself as a small side project.
With browsers, this is a lot more difficult. There are perhaps three modern browser engines, which are mostly open source but also very large pieces of software. There are no books or tutorials explaining how to develop browser engines. And the debugging tools in the browser only tell you how often a "DOM update" or "render" happened and perhaps how long it took.