I expect it's much the same use case as for asm.js and WebAssembly — just a different solution to the same problem. The intention is probably for it to become an easier way to port software to the web, although it seems like a lot more work will have to be put into it for it to be remotely viable for many programs.
We already work with asm.js, and I've gotten some WebAssembly prototypes running under Browsix as well. Browsix is nicely orthogonal to those projects -- WebAssembly lets you compile existing C/C++/Rust code to run in the browser with almost no overhead, and Browsix gives you the environment your program expects (pipes, sockets, a filesystem, subprocesses).
