How can I debug a crashing application on OS X?

I have a game installed from Steam on my Mac (Crusader Kings II). The most recent patch from the developer has been having crashes and freezes on my Mac, and I'd like to help give the developer as much debugging information as possible (I'm an iOS developer myself).

One of the problems with the game involved the game completely freezing up. To assist in debugging, I used the Time Profiler from Xcode Instruments and attached it to the game. When it froze, I could see what exactly was using up processor time, and I've reported this to the developer.

However, the other problem with the game is a hard crash to the desktop. Normally, when applications (like Xcode) completely crash, OS X will give me an error report that will include useful information, like the stack trace. However, when this game crashes, I get nothing. It just completely disappears. The process is no longer in the Force Quit list, but I also get no crash report.

Is there any way, using Xcode Instruments, or any other means, to determine exactly what state the application is in in the instant just before it crashes?

My computer is a Mac Mini (late 2012 model) and I'm on OS X 10.10.1 if that matters.