The Dappy browser is an open source browser that implements the Dappy protocol. The name system is not the only thing that changes, dappy browsers also deals with CORS/cookies/CSP in a different manner. Simply check the first sections of this document to get an idea.
The Dappy browser is built on chromium+electro, it is able to display every website that currently exist and deals with HTML/CSS/JS just like regular browsers.
Anyone is free to grow the dappy ecosystem by developing a browser on rust/go/haskell, to fork existing browsers and add multi-request support.