...because the goal of the Internet Archive is to get playable versions of archived media into your hands, and Chrome/FF/Safari/Edge/etc represent a powerful & free, execution target that everybody already has.
Besides -- and this is key -- they're not rewriting it in Javascript. Javascript (via Emscripten) is a compile target for the code they already have.
Those who have read the article know this; it's right there in the article:
I know that it sounds like porting things to Javascript
is crazy. I find that people think we’re rewriting things
from scratch, instead of using Emscripten, which compiles
out to Javascript as a target (and later WebAssembly). We
do not write from scratch.