All the information is collected anonymously – it doesn't say who the visitors are.
Apart from that, the site uses several third-party services which may affect visitors' privacy:
Books from Amazon
As an Amazon Associate, al-bab earns money from qualifying purchases. When al-bab links to books which are available from Amazon the links usually contain a code which tells Amazon you have come via al-bab. This is so that al-bab can receive commission under the Amazon Associates programme if you decide to buy the book.
Facebook, Twitter and other social networks
The blog posts and some other pages at al-bab include buttons for sharing them on social media. If you click on the buttons, whatever use (if any) that Twitter, Facebook, etc, make of this is outside al-bab's control.
To allow visitors to post comments on blog articles and some web pages al-bab uses a discussion system called Disqus.
This uses embedded code provided by Disqus which, again, al-bab does not control. Disqus anonymously tracks visitors to pages and also remembers who you are if you log in to any Disqus service.
Logging in to Disqus can be done in various ways, including via Facebook. If you log in via a social network, Disqus will be able to link your activity to that network. In this way, your Disqus activity may be personally identifiable.
In any case, all comments you post are also publicly visible on the internet and al-bab requires everyone posting comments via Disqus to verify their email address.