I agree with Tommo781. While it's hard to say if it will count, I think it should. At least part of the stay occurred during the promo period. I don't think the date of check-out matters (i.e. I believe a stay that begins on Sept 5 and ending after the promo ends will also count since the first night falls within the time period).
The terms & conditions say stays made "between May 24, 2016 and September 5, 2016." I see nothing indicating that a stay has to begin on May 24 or later. I say it counts. I suspect Marriott will say so too. At least I hope so. Let us know when you complete a 2nd stay (based on this one being the first) if you get your 2,000 points.