The launcher window starts, but when I click "Play Game", I see a gray window pop up for a few seconds, and then it disappears.

Video: youtu.be/kO4dlSngcFg

Same here. Wondering if a Windows update has broken something!

After some digging, it seems if you have speech recognition turned on the game won't start. How silly.
I can't post links, but check the Matrix forum for WITW, within Tech Support Channel, look for a thread titled "WITW Steam Version Crashes"