This conversion (or any other similar exe to video conversion) is mainly searched by users that would like to convert Flash videos (made for example with Flash Projector) to the original source video, which in case of exe to avi conversion is AVI format.
The process usually follows the pattern of recovering SWF video (.swf) from the executable (.exe) via one of the many available SWF tools (check out exe to swf conversion entry) and conversion of the said .swf file to any of the desired video formats, in this particular case using swf to avi converters.
You can also try to use some screen recording tool, open and play the .exe file (with the video) and capture it again to actual video file. Not perfect, but at least doable. The resulting quality may not be the same as the original though.
In any case, you should be always extremely vigilant when dealing with unknown .exe files, you can easily infest your whole computer and in the era of ransomware potentially compromise your valuable files.Open EXE file Open AVI file