Oh boy... Where to begin?
Well for starters, your source of information is faulty. The Wall Street Journal is a division of News Corp, the "news" organization headed by the infamous conservative, Rupert Murdoch. NOTHING that comes out of that conservative propaganda machine can be trusted as objective fact. FOX News and the New York Post (two other divisions of News Corp) are notorious for spin-doctoring and in many cases outright lying to the public in order to discredit liberal views and give legitimacy to conservative ones. While the WSJ isn't quite as bad since it primarily focuses on economic issues, it is still subject to bias and will tailor stories to discredit progressive or democratic administrations.
As for the actual point of the article, I am in no way a friend to the Taliban. Their brutal and oppressive policies make me sick to my stomach. However, while it is true that the administration did not refer to the Taliban as terrorists in this instance, it's important to note that they never have. The Taliban was the fundamentalist Islamic regime that controlled Afghanistan prior to being overthrown after the events of 9/11, resulting in them forming an armed insurgency against us for the duration of the war. And while people the world over have decried the massive list of human rights violations the Taliban has accrued over the years, neither the United States government nor the UN has officially declared the Taliban to be a terrorist group. Whether you agree with this or not is another debate entirely, but this was the policy long before Obama came to office.
So why would they make a big deal about it in this article? My analysis: it's an alarmist smokescreen. Especially since the recent Charlie Hebdo attacks in Paris, FOX News and the other divisions of News Corp have been trying to capitalize on the idea that Obama is "soft on terrorism". While this is not the case, they have had success pushing this idea primarily by using articles and "news stories" like this one. This particular story aims to prey on the ignorance of its readers, many of whom likely believe that the Taliban and Al Qaeda are one in the same. They are not, and the latter is the one that is actually recognized as a terrorist organization. But by implying that the Taliban was once considered a terrorist group (again, false), they give false legitimacy to their conservative narrative, drumming up disapproval for the current administration and, by association, the Democratic Party.
Ah... Deception at its finest.