Hi,
I've just read a bit of the fraps FAQ, having never used fraps. http://www.fraps.com/faq.php
They say that the codec required for playback is installed when you install fraps. That is why when you converted to quicktime and the other machine had quicktime it played without a problem.
So by installing fraps on the other machine it will then play the avi. However like previously suggested and done I recommend converting to another codec.
Regards