Actually LogMeIn is not really running in a browser, it is a Win32 app at its core and just uses the browser to launch itself. So it should be possible to have UI and options to dictate which screen goes where. They can copy some of the UI and logic from tools like 'Input Director' and Synergy.
I bet it just requires a lot more bandwidth to send that second monitor and also some more code in their video driver hook.
Would still be nice to have.