Thanks for the great question. With Slingbox a router is needed. Without the router we can not even see the Slingbox over the network either over the web or not. You would want to connect the Slingbox to a router and the computer or mobile device to the same router. This would be the most effective way of watching the Slingbox. With this configuration the Slingbox would first connect over the Internet and than if found on the same subnet it would start streaming over the local network and not eat your bandwith. If you are outside of the home this would not be the same result.
Hope this helps,
Sling Moderation Team