Why? Simply because browsers need to be compatible with literally millions of existing sites. While game engines only need to be compatible with it's own current major release.
If we could drop all the baggage of current web technologies and build a new browser engine supporting new APIs, then it would be easy (comparatively speaking).
The issue isn't so much the technologies available (though I've often cited reasons I'm unhappy with the status quo of web technologies) but more than game engines don't need to be compatible with every game in existence. Whereas web browsers need compatibility with every website.
It's compatibility that's hard.
Another example of how compatibility is hard is looking at how operating systems support older applications. A lot of the problems Windows has is due to its commitment to backwards compatibility. Whereas Apple take a different approach and expect developers to port their applications to newer releases of macOS.
Game engines run only their own games, each has its own specializations and choices, and they have and need zero compatibility with each other.
There's also the difficulty of getting your development money back given the dominance of the two big ones, chrome, and Firefox.
It took google, with all of its resources, years to write chrome to give an example of how hard it is to write one.
Writing a game engine is much easier in getting resources and payback.
It is a exciting future.
