These small libraries and their buildings are inspirational and I look forward to more public libraries creating outdoor spaces where the people of a given community can use books and other media at their leisure. One other great example is the Library Reading Café in York, UK: http://www.guardian.co.uk/uk/the-northerner/2012/jul/12/libraries-universityofyork
While the internet does offer access to, well, a lot of information, I would argue a few points:
1. While there full-text versions of books in the public domain available via Google Books, one cannot "borrow" books for free online except via actual libraries, all other methods of reading books online involve a pay wall.
2. There is a vast difference between knowledge and information. Even amidst all that is available on the internet, the resources found there are often not vetted in any way, I would argue that the knowledge available is in the forms of video and editorial writing like blog posts -- but there is a lot more "stuff" (fluff!) out there that falls neither into information nor knowledge categories.
3. Neil Gaiman is widely quoted as saying, "A Google search can return 10,000 results; a librarian can give you the right one." People who are knowledgable about what resources exist can trump the most powerful algorithm.
4. SO MUCH web content is not available for free, such as back issues of newspapers, magazines, and journals -- all of which ARE free to you through your public libraries which pay subscription fees (with your tax dollars) so that you may have access to these and all kinds of information resources related to healthcare, finance, and fun content like music and movies.