I don't think so. Braess' paradox is about how a Nash equilibrium may not be the optimal solution, and so closing a road might result in a more optimal Nash equilibrium. But this article is talking about how closing a road is causing there to be literally fewer cars overall on the road than before. The traffic is still higher on the surrounding roads (which suggests that the individual commute times for those roads are in fact getting worse, because higher density usually means slower speeds).
Edit: I suppose if you add alternative forms of transportation to the "network" that you're analyzing, it's possible that this could be viewed as a form of Braess' paradox, but only if the overall average commute time has in fact decreased. There's nothing in the article to suggest that the overall average commute time, covering both cars and non-car travel, has decreased.
