WinJS started out as a tool for creating Metro apps with HTML5 and JavaScript as an alternative to XAML and C#. I don't know if Microsoft is now spinning it as a general purpose web tool but that was not its original purpose. And this has always been explicit. The default ASP.NET MVC template, for example, bundles Bootstrap and jQuery. And if you look at the SPA examples they're all in tools like AngularJS and Knockout. In fact, in one of their build sessions they teach how to create a SPA with AngularJS. As far as I know the ASP.NET team has never used WinJS.
So it wouldn't surprise me if this library didn't work great on the web on any browser because it wasn't created for that purpose.
At first I thought it was a cross platform app building something-or-another (kinda like Xamarin), but now that I actually am building it and playing around with it I see that it's something else entirely.
I'm actually glad this happened though. Seems like MS is finally rallying around C# as the defacto language for building apps (as opposed to Visual Basic or even Visual C++). This project might succeed (or at least find a nitch) among developers who are building touch centric web applications.
So it wouldn't surprise me if this library didn't work great on the web on any browser because it wasn't created for that purpose.