Are the ES6 syntax compiled too by the TypeScript compiler? Or do I have to use an additional compiler (Babel)?
You need additional compilers that downport your code from ES6 to ES5.
TypeScript is pretty smart and will do most of the work for you (i.e. translate
var or arrow functions to standard functions with right scope and bindings).
It sometimes fails though. For instance if your code requires
Promises it won't compile until you set the ES6 target.