This would be an example of crowding out because the government is supplying the books for people to read. There is an increase in government spending and a decrease in the money being spent in private companies which are the bookstores. People do not need to go to the bookstore to purchase these books but instead go to the libraries and check them out for "free." This burdens the private companies because they will potentially have a decrease in sales.
It is important to keep in mind that in order to build new libraries and stock them with books, they need money. This money is going to come from tax increases.
This is not the way that the term is used in textbooks I have taught from. The texts I've used use this term to mean that private investment has gone down because of excessive government debt.
However, the idea is pretty much the same as what you are talking about. You are talking about a situation where what the government does, in essence, competes with private enterprise.
So if your text and/or teacher uses crowding out to mean this kind of more generic thing, this would be a case of crowding out.
This phenomenon is definitely the phenomenon called "crowding out" in economics. Perhaps the phenomenon could have been describes as something like crowding out, if sale of books had resulted in increasing the prices of books sold to individuals. However there appears to be no reason to believe that this actually happens.
I do not have the statistics on value of sale of books to individuals and to libraries. But if the value of sale to the libraries is more than the sale to individuals, it simply means that, on average, the value delivered to ultimate consumer, the reader, by a book kept in library is more than the same book purchased by an individual. The obvious reason for this is that one copy of a book in a library is accessed and read by many more people than a copy purchased by an individual. This difference more than offsets generally higher price of hardbound books kept in libraries, and the cost and efforts the readers incur for referring to and borrowing books from libraries.
Another related explanation of higher volume of sale of books to libraries is that a very large number of specialized books are published that are costly to be purchased by most individuals. Frequently one person may only want to refer to a small part of the book. Further, the total number of books one person may be required to refer for a specific project or a task like writing a paper or a dissertation may be too large. A typical person may find it beyond his or her means to buy and keep all such books. In addition, the the libraries make a large number of books readily available to the readers, including many books that may be currently out of print.
Funding is extremely important for public libraries and physical books will be used by many people for years to come. Much of the funding comes from community sources and fundraising and is necessary for any non-profit organization.
However, the increased use of digital books, e-readers such as the Amazon Kindle, the Sony eReader, and the new iPad by Apple is making the use of actual books much less desirable. These e-readers are very convenient, portable, and, for those who buy books, the price is very reasonable. Textbooks are now being used on e-readers, especially at the college level and this practice will move into the Pre-K through 12 levels more and more in the years to come.
Conversely, some people WANT to hold a real book in their hands and like the ability to write real notes, with real writing instruments so it will be a long time before books "go away!"