So Overwatch just got an update (actually a few, it seems) today, 7/21/16.
With this update, Dxtory doesn't seem to be able to run at the same time as Overwatch. I've already contacted Blizzard support but they couldn't offer much help aside from "Close Dxtory".
What's particularly odd about this though is, Overwatch will continue to run if it is opened and then Dxtory is opened.
Anyone else experiencing this? And does anyone have a fix?
I went to Advanced Settings and checked "Delay Hook" and it seems to have fixed the problem.