No, Yahari Ore no Seishun Love Comedy wa Machigatteiru. Zoku is simply the second season of the show Oregairu, and not a remake of the first.
While both are adapted from the original manga, the current two seasons of the anime are chronologically ordered, following directly on from one another.
This is clear after comparing the episode synopses of both season 1 and season 2 on their corresponding MyAnimeList pages.
There may well be some similarities in the two seasons, as shows often provide throwbacks or other references to earlier works, but since the plot itself continues on, this isn't enough to classify it as a remake.