Turns out that .camrec files created by Camtasia are actually zip files that contain the .avi that was recorded. You can use a program like 7-Zip to extract the .avi file

And if you want to save some space, you can always compress that .avi file with WinRar. It looks like the .camrec zip file is not compressed - however I've been able to take a 5GB+ avi file from Camtasia and compress it down to under 400MB.