To be fair, if you read the British Council website carefully, the library bit only refers to teaching materials and children's books. They had a good collection, but it was only being used by expat Brits, so they decided that their duty was to the local, ie Qatari, population, and got rid of the fiction library in order to focus on teaching and reference.
The collection went to the Doha Players, but was destroyed in the bomb attack.