A compiler written in itself only proves that a language is good for writing compilers. A browser engine on the other hand touches huge swathes of the big problems faced in computer science, and puts severe demands on a language in terms aiding the production of fast, concurrent, and safe code that can be maintained at scale.
It's still a fair amount of code, and means dealing with less CS-y things but still practical things like command-line arguments, data structures, file handling...
To be fair, commandline arguments and file handling fall under the heading of "things that get your language get eliminated from ever being taken seriously if they're not straightforward to do". Data structures... how do you figure they're "less CS-y things"?
I'll blame the lack of tea. Data structures are quite CS-y. The point is, you have enough complexity in a compiler to find out a number of weaknesses in your language if you self-host, even if it doesn't cover everything.
