AppGyver employee here – the part from Ionic we forked is the great CSS defaults, so it's more like "Ionic CSS + AngularJS + Cordova + AppGyver stuff". What we bring on top of the CSS framework is native navigation, native UI components, data etc.
I found the CSS to be one of the worst parts of Ionic.
"Oh did you want to make a change? You'll need to declare it six levels deep and !important"
I think Ionic works with or without Cordova. There is a Cordova plugin to Ionic.