I currently write compilers that target JavaScript and have looked a TypeScript a lot for something like this. In practice, TypeScript isn't actually strictly typed. There is a ton of TypeScript code out there that does stuff like run-time prototype manipulation (mixins, for example), using arbitrary objects as hash tables, and liberal use of the "any" type.
So either you cross-compile a JavaScript VM to be able to handle everything (super slow and bloated, especially without the ability to JIT compile executable code) or you pick a small subset of TypeScript to compile, in which case it wouldn't really be TypeScript at all.
Plus TypeScript doesn't have integer types (only doubles) so it would generate pretty inefficient code. JavaScript JITs do a lot of work to turn usage of doubles into integers based on run-time behavior that is unknowable at compile-time.