Going to have to start by proclaiming that several other things are human rights before you get to Internet access.
Access devices are a human right. Electricity is a human right. Access to telecom lines (of some sort) is a human right. Access to mobile or a spot to plug into is a human right. Transistors are a human right. Storage is a human right. Some kind of electronic or digital display is a human right.
First, this is a set not a list so it's nonsensical to rank those in importance.
More to the point, I don't read that proclamation as "everyone is entitled to internet access".
I read it as: no-one (specifically government) should be able to take away your access to internet.
The difference is not that subtle.
It's important because it counters a growing world-wide tendency to take away your access after some minor infractions like copyright infringement.
It rightly recognizes that access to internet is almost a necessity to conduct your daily business (in first world countries, at least) and denying that access creates incredible hardship and can ruin lives (ruin not at all rhetorically; if you, for example, make money via etsy or odesk, taking away this income might push you over the poverty line).
There is a difference between the right of not being prevented from doing something, vs. the right to force others to facilitate someone doing something. The right to acquire and use something at your own cost as you see fit is one thing, forcing others via state police powers to pay for and provide those things to you is another.
Know the difference, lest people argue about different things.
Access devices are a human right. Electricity is a human right. Access to telecom lines (of some sort) is a human right. Access to mobile or a spot to plug into is a human right. Transistors are a human right. Storage is a human right. Some kind of electronic or digital display is a human right.