I'd like to ask whether the Aurelia JS framework can be used as replacement for i.e. Ionic in hybrid app development. I have seen some tries, how to integrate with Cordova, but from their pages it is not really clear how it should be done.
You can just use Aurelia on Cordova as you would in a regular browser. That's basically what your linked article tries to tell. Get started with Aurelia and host it in Cordova. But this does not solve what you might expect as a replacement for Ionic. Basically you would have to build this layer of abstraction yourself or use another UI framework that suits your needs.
@EisenbergEffect talked in comments about the "secret" project named Aurelia Interface that will probably be the replacement (Aurelia + Cordova) for Ionic (Angular + Cordova). But currently not too much is available in the wild about this.
http://blog.durandal.io/2015/09/05/aurelia-early-september-release-notes/#comment-2242530528
https://twitter.com/eisenbergeffect/status/627163846709526529