Seems cool at first glance! I've never heard of Handshake, will be looking at that more in particular.

So I see the address in the screenshot starts with federalist://

Is it possible to access these sites with a normal web browser from the internet too?

I do think there is a way - since the beautiful WebTorrent (https://github.com/webtorrent/webtorrent) can do so in browser. I'm keen to see something like this in a normal web browser (if possible as an extension even), hopefully developed by someone with better skills than me haha!