The seventh season of GoT -- the one that just concluded with some epic, dragon-fueled developments -- premiered on July 16, but for a show to be eligible at the 2017 Emmys, it had to air episodes that would be for consideration between June 1, 2016, and May 31, 2017.
Technically, the last four episodes of season six do fall into that time frame. However, the television academy instituted a rule about what they refer to as "hanging episodes," meaning those four episodes are technically considered to be a part of the previous year's eligibility window and are excluded from consideration this year.
It's a tough blow for the show, especially considering it's the first time in years that the show's cast and creators won't be vying for a golden statuette at the star-studded awards ceremony. However, with a record-setting 38 Emmys, the show isn't hurting for more hardware, and it's a good opportunity for other shows to earn some glory.