This is most likely due to the compression software (codec) used to create the video. Some video capture cards and video editing programs use proprietary software to compress video files - you need their codec installed in order to read that file.
The ASUS capture card ships with ULEAD's Video Studio which includes a full range of output options. When you create your video file, look for a setting that alows you to select a codec. Select one of the Indeo codecs and your video will be playable on reasonably up-to-date windows pc's. (Sorry, I'm not up to speed on Macs.)
Another possibility - if you're trying to share the captured avi file without "rendering" it through the ULEAD program, you won't be able to read that avi file on another pc unless it also has the ASUS card installed. Instead, use the bundled ULEAD program to create the final video file.