TL;DR This was never intended to be a full season. This is just an intermediary series to keep the audience's interest while the real season 2 can be finished once the Manga is sufficiently ahead.
MyAnimeList: New 'Nanatsu no Taizai' TV Series Announced for 2016.The page clearly states,
The announcement does not specify whether the new series is a sequel.
This has been done before for example with Magi. Post season 2, several episodes relating to Sinbad's history were released so that the Season 3 had enough source material.
This is a original mini arc written by the author himself. According to the discussion on MAL.
This is basically a movie, but instead of releasing on theaters, it’s been released on TV in 4 episodes....
Anyhow, I’m cool with that as long as it is written by the mangaka (which it is). Hopefully we will get an announcement later this year (or maybe next) about a possible sequel in 2017.... I doubt there won’t be one given the great success of this franchise.
Also, this was never announced as a second season to begin with, so I’m not sure why some of you’re surprised by this... It was announced as Nanatsu no Taizai (2016), not Nanatsu no Taizai Second Season (2016) from the very beginning. If this was indeed a second season, they would have added that to the title the day it was announced, simple as that.
Anyway, looking forward this original mini arc story written by Nakaba Suzuki himself.