It is unlikely you will be able to just do this with Node-Webkit. Especially since the official webkit does not support AVI. Your best bet is to use an external application like libav (avplay) or use node to serve a webpage that has a player capable of playing the content and just let the users browser do the work. (Flash is likely still the best way to go, video.js is a good choice)
The alternative is to convert the video to one of the supported formats. I would recommend mp4. (Once again libav (avconv) comes in handy here.) This still assumes that Node-Webkit has implemented full HTML5 support. (I am not sure what they have completed but I am guessing it supports the video element)