@zezba9000 right, it doesn't currently use WASM, but I'm guessing it will (might be a wild guess which is completely wrong). Mostly because of the recent title change ("Support for running C# on the web browser."), and also the last comment in the readme about WASM, and the fact that there doesn't seem to be any other actively developed repo from xamarin that comes close to this (that I saw).
They expose DOM c# APIs there which can be made to work against WASM instead of PepperSharp (which I'm not sure what will become of it as Google deprecated NaCl in favor of WASM).
I would definitely love to see more concrete details about WASM development, so we wouldn't need to resort to guessing.