Interesting. I'm not sure you install it to your Wii. From github:
"The Browservice server uses
CEF (Chromium Embedded Framework) to run a Chromium browser instance that renders the browser view into an off-screen buffer. The browser view, combined with a control UI bar, is then compressed as a PNG or JPEG image and served to the client using an embedded HTTP server. The client browser runs a JavaScript application that requests and shows the images."
So when you're running the server (which you setup on a PC), you just point your Wii's web browser at it (the "Javascript application"). Within that application is the URL field and other stuff.
Important note: no on screen keyboard. You have to use a USB keyboard with your Wii if you need to type anything (like a URL)