In his presentation he mentions that it can be compiled inside the web browser, however, Microsoft did not supply the necessary tools/examples showing you how to embed the compiler inside your web page (as opposed to having it compiled on the back-end). Fortunately, github has a nice example, proving that it can be done. I installed the sample on my server so you can simply test it live if you want. For some reason the demo only works on my phone if I “request a desktop site”. But requesting a desktop site proves that the demo can compile just fine from the phone.
I may put it through the paces and change it a bit as I am rather curious about this new language myself. Compiling TypeScript on the client, means that the server does not need any special support or plug-ins or compilers installed. It will just work. However, you might want to consider compiling it on the back-end to protect your valuable code.