I think "Big Web" is a profile hosted on "cloud infrastructure" owned by a company with public stock. Whereas "small web" is a website you build/create yourself and host on your own server?
This image could have some smarts to either punch the right holes through the the router's firewall or do something even more clever with a peer-to-peer mesh network.
At the end of the day, what one would have is a website of their own that they control within their residence. It would foster a lot of this small web spirit and be very cheap to bring to market and maintain.
If anything, the "dumb delivery mechanism" only became slightly more trustworthy?