Quite a bit, actually. Since 2007, we've gotten Javascript JITs, Canvas, WebGL, consistent box models, consistent event models, flexbox, CSS transitions & animations, CSS transforms, localstorage, IndexedDB, websockets, HTML5 audio & video, history.pushState, and several other features. And components (custom elements + Shadow DOM) are coming, and already implemented in some browsers.

Pretty much anything you could do in a native Windows app in 2007, you can do in a webapp now, except pwn your computer. Only problem is that the goalposts have moved: now everybody expects you to be able to do it on a phone as well, as well as access the camera, accelerometer (which you can do on the web, actually), contacts, calendar, and bluetooth hardware.

Perhaps not in the limitations of the DOM, but how we deal with it is changing.