We do not currently support any viewing methods with the Xbox 360. You could try the SlingPlayer Facebook page to see if that works.
I have moved this over to our enhancement request forums page to let everyone know what method of viewing you are looking for.
Thanks for the request!
To answer your question no the Slingbox cannot be streamed through the Xbox 360 web browser as the browser is a mobile based browser and is not supported.
I will add a link to the supported options to watch your unit:
Hope this helps,