The G+ comments seem to indicate that they're using the browser's event handling in some way.
Plus the browser runtime still gives you things even if you're going the pure-GL UI route: networking, a JSON parser, a database (Local Storage), cookies and session management, a (arguably awful) security model... how is the browser "dead weight"?
All those things are easily provided by libraries for every language with every API imaginable. The strength of a browser is HTML & CSS.
And I called it dead weight because we're talking client-side offline UI here, so things like cookies and session management are irrelevant. But the dead weight is going to come from the bulk of the browser code that is HTML/CSS parsing, webkit/blink, the graphics model that's not being used, font support that's not being used, etc... Those things you list are all really small pieces.
I strongly suspect the PS4's UI is neither truly client-side nor offline.
I don't disagree that there's a lot wasted but I'd probably have made the same trade-off given the circumstances.
The PS4's UI isn't particularly resource-constrained as far as I know and it's often easier to start with a familiar environment with everything and the kitchen sink than to start with nothing and hand-pick blocks along the way. Plus based on Sony's past in-house UI performance, the "glue libraries together from floor 0" approach wasn't working out for them.
So far the PS4's UI is getting good reviews and is generally described as "responsive" so it sounds like they didn't really lose - in a modern device where you'll end up porting a browser anyway I don't see why using it for UI is such a sin.
Plus the browser runtime still gives you things even if you're going the pure-GL UI route: networking, a JSON parser, a database (Local Storage), cookies and session management, a (arguably awful) security model... how is the browser "dead weight"?