The cable channel only decision was made in 2013. In 2016 they could just shut down Al Jazeera America, and stream the main channel. (It looks like that is what will happen.)

You do get data from internet tracking, but it is based around your activity and some correlation (eg geoip). Note that Al Jazeera would only get information about their own activity. There are various services that aggregate at a higher level, but they do cost money. I can't find any now, but there were a few companies that had a service you could ask about the current user and they would return likely demographic information.

That all matters if you are trying to sell the advertising yourself. If someone else higher in the user visibility chain sells the ads (eg google, facebook, yahoo) then they already have the comprehensive tracking and demographics. But advertising isn't that profitable and those guys will take a big chunk of the revenue, while you remain beholden to them.