My personal guess is that there'll be two main ways end users use WASM apps. One will be the browser naturally, but with a push for PWAs. If you go to an app URL and like it, you can "install" it from the browser menu. This isn't WASM specific and sites like Twitter and Instagram already do this, but I suspect we'll see a bigger push from players like Google to make WASM PWAs.

The other main way will likely be "native" apps that are based on Electron or a similar framework. Electron is already Chromium based so WASM support will likely be included in Electron (if it's not already) and devs will make "native" apps that way that are downloadable, or installable from OS app stores.