I think one possibility is that the game is not crashing but you're pressing one of the two "panic" buttons meant to allow you to hide the game quickly in case someone enters the room and you don't want them to see what a fun game you're playing. This link explains how it work:
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Even then, if Windows won't delete a file because it's running, you should be able to find it in Task Manager. I've never had a program running I couldn't find there, so that's quite strange.
What is the red icon you mentioned? Both ktt.exe and KronosTimeTitan.exe use blue circle icons. I'm not sure what icon would be red.