The problem is that the DOM is a hard upper limit on performance compared to what the performance of an unsafe language (asm.js) is. It is massively complex because it must perform every UI task in the browser and simply moving around DIVs doesn't give you a feel for its the performance in complex scenarios.

If you think about how native applications perform and then imagine every one having to go through a DOM interface and every button and UI interaction being composed of DOM elements and re-styling these elements on every interaction you get a sense of what the problem is. There is simply no way to get the DOM to do something it wasn't designed to do, which is to be a document display interface and not a general graphical user interface. You have to clobber together a lot of interactions to get the desired behavior and not only does this increase the overhead for both your program and the DOM you are going to hit cases where the DOM isn't optimized.

This doesn't mean that the DOM is inherently slow. If you tried to offload the UI work onto javascript you wouldn't get the performance benefit of doing that on Asm.js or NACL. You really need unsafe code to solve this problem. Asm.js and NACL are only useful if you are going to do this; targeting the Canvas and WebGL gives you the ability to do that.