Any work on that in progress?
TypeScript is designed for the JavaScript runtime, with the only difference being additional compile-time type checks. The runtime behaviour is basically defined as the JS runtime behaviour, so any alternative engine will have to be a full JavaScript engine.
That said, there are some projects that take a subset of TypeScript and run using different implementations. One example is https://github.com/AssemblyScript/assemblyscript However, being a subset, the available functionality will be a lot more limited.