This takes a little while because for some reason they're doing remote rendering and streaming rather than rending in the browser with WebGL.
Re: the sibling comment, I had to switch the Chrome to see the button, but I don't know how patient I need to be, or what the interface is supposed to look like once it's ready.
Edit: ok, took a couple of minutes. That is way more awesome than the initial demo. The map even includes the ready room and conference room of the Enterprise D.
Once it's loaded, it'll change to a 3D flythrough of the selected bridge with a "Click anywhere to continue" message at the bottom. Clicking stops the flythrough and lets you move around (with fairly standard FPS controls).