I do wonder how well this would integrate with SPAs - seems like it would be great for testing events/handlers/etc, but might be weirder (or at least possibly more work than just refreshing) for testing app starts and the like.
Support for clients are definitely coming, JavaScriptCore and Node would be awesome, but one step at a time, trying to support multiple protocols before 1.0 could become overwhelming very quickly.
I don't believe BrowserSync does 'hot code loading' like Amok is doing.
Hot code loading is when you update the running code without reloading the page, preserving any state in the program running.
If you watch the start of the Amok video you'll see author changes the elasticity value but the timer at the top keeps ticking and the ball doesn't reset to the start position like it would do if the page were simply refreshed. (BrowserSync refreshes the page when JS is changed).