The AVI Player inside Jinx! depends on the Video for Windows API, so you need to install the needed VfW codecs for your AVIs. The best starting point ist to install the ffdshow codecs: http://ffdshow-tryout.sourceforge.net/
Be sure to activate the „VfW Interface“ while installing to get the VfW codecs. After installing the codec start the VfW configuration. Here you can activate a lot of codecs which will not get activated automatically. Choose the decoder tab, click in the left pane on codec and you can simply choose a right click in the right pane and select „set all stable formats to libavcodec“. This will activate nearly all codecs you will ever need to get your AVIs running within Jinx!
When you try to get the VfW Codecs into Windows 8(.1) you should use an older release, because there is a bug in the newer releases from ffdshow: ffdshow_rev4499_20130104_clsid.exe