webkitSpeechRecognition needs a back-end speech recognition system.
Chrome may use Google's speech recognition system. So we can use webkitSpeechRecognition on Chrome without any hassle. But on others even though it is based on webkit, It may not work properly.
I think it's difficult to use speech recognition feature on node-webkit before supporting Google's or someone's engine.
Also CHANGELOG 0.8.0 / 10-30-2013 says
- undefine window.webkitSpeechRecognition before it's supported