AVI is not a video format, it's what they call a container or generic extension for video. The codec that was used to encode the video can be many different ones; divx, DV, mpeg etc. If you don't have the codec installed then applications like WMM that use system codecs will not be able to play them. Also note that WMM can be problematic with some codecs so it may never import it.
VLC has it's own library of codecs and doesn't utilize the system codecs, that's why it will play in that application.
This tool has not been updated in a very long time but you can try this first:
GSpot Codec Information Appliance
It should tell you what codec is required, find a reliable source for the codec and install it. For example if it's encoded using Divx got the Divx site to get it. On a side note be very careful of codec packs that contain multiple codecs as they can cause issues.
Once installed see if WMM wil open the file. If it doesn't I'd suggest either using a tool to convert to WMM compatible format like DV or get a real editor.