The same reason the Open qualifiers close the day before listed. Since the game runs on PST, things that end on 8/31 actually end at 3AM on 9/1 EST. So they show the close date as 9/1, because apparently they figure we wouldn't be able to figure it out ourselves, I guess. WGT staff corresponded in e-mail with me regarding the Open qualifiers, but have not fixed the issue. In grammar, when something is listed as X-Y, that reads as X through Y, but WGT hasn't figured this out yet. But if it says Aug 1st-Sept 1st, what that means grammatically is that the tourney will run until it is no longer Sept 1st, but to WGT it means until Sept 1st arrives PST.
But yes, if a tourney is listed as running - Sept 1st, then any time you play on Sept 1st should count. One of these days, maybe WGT will fix that.