Sure, game engines are really complex and impressive, but the same is true of a lot of other kinds of software. If you work on websites, have you thought about how much processing goes on when loading and rendering a page?
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.
Whilst true, your simple renderer analogy does not work because it is like me saying that if I can create a program to draw some scrolling text then I can create a browser. I presume you have not had to optimise GPU graphics code whilst maintaining compatibility on multiple GPU vendors with a common code base?
One game engine is not the same as another and therefore not suitable for bulk comparison with any particular thing. Each game/graphics engine has their own set of requirements, and quality level, and the level of understanding required to "understand" what is actually going on.
If you are restricting to AAA, I’m not even sure if that holds. There are a good amount of big teams that use UE4, I think I’d go with Frostbite due to the sheer amount of titles that EA pushes out that are now based on Frostbite. It’s certainly more big games than UE4 is shipping. I’d probably put Ubisoft ahead of them too with their internal engines.
a) build their own internal engine
b) pay licensing fees to not disclose what engine they're using.
For overall game usage, however, I'd definitely say Unity is most used, with UE4 coming in second
They're actually similar in some ways -- there are a handful of browers and a handful of AAA game engines, and they're all either open source or at least licensable source.