David Benioff and D.B. Weiss have expanded on previous reports that Game of Thrones is fast approaching its endgame, with their preference being to end the series 13 episodes after the end of Season 6. Their previously-mooted suggestion was a seven-episode seventh season followed by a six-episode eighth season. However, in a new interview with the Hollywood Reporter, they have confirmed there is some flexibility.
They now say that the story could be concluded in 10 episodes - potentially a seventh season of ten episodes as normal - but may require as many as 15. In that case we may see both the seventh and eighth seasons shortened to spread them out more evenly (so maybe eight episodes in Season 7 and seven in Season 8). They're currently mapping out how the story ends - and most of the scripts for Season 7 should have been written by now given they start shooting in just a couple of months - so there should be a firm plan in place shortly.
This does explain why the show was not renewed for an eighth season, because if they do decide they can get the story done in just 10 more episodes, they won't need an eighth season. However, my gut feeling is that 10 episodes is just not enough to wrap the story up and there will be a shortened eighth season of some kind.