WhatsApp is going to add new features to its web version which is known as WhatsApp Web. The desktop version of WhatsApp will allow you to change the privacy settings like Last Seen, About section and Profile Photo etc. At the moment WhatsApp Web does not allows you to change any settings through desktop app or the browser version. You can also change then through your phone.
According to some reports WhatsApp will add these features with some new update. This new multi-device feature will make WhatsApp Desktop independent from your phone. WhatsApp web will allow you to change the privacy settings and also change the list of people who can view your personal information. It is still not confirmed that the feature will be available to everyone but it will roll out to beta testers very soon.