As the site mentions elsewhere, they have a relatively power-hungry fiber router that needs a constant 10W, currently still running on the grid. In that sense, the website isn't entirely solar-powered. This seems to be the state of things going into the future--computation may get more efficient, but pushing signals to far-away distances will always take more power!
To add an anecdote, those Comcast modem/router combos get really hot and are constantly running their fans. They probably have some pretty poor software on average and aren’t running power management daemons.