The slingbox needs an internet address. Your Internet Service Provider provides one wide area network addresss to a modem device when you purchase an account with the ISP. The router then provides a means to share that internet access with many devices (desktop computers, laptop computers, iPads, Tivos, Slingboxes, etc) by building a local area network . To attach one -- and only one -- computer directly to the modem, you would have to tell the modem to "clone" the Media Access Control ID of the modem -- The MAC ID of the modem is the unique number that is registered with the ISP to receive the internet signal. While possible, this is not a good thing to do security-wise, since this exposes that computer directly to all of the potential bad things out in Internet land.
I don't think the Slingbox has this cloning capabilty in its software, and besides, putting a router between your modem and EVERY device you might want to attach to it (even if it is only one device) is a much safer approach. Most routers come with 4 ethernet ports built in, but if you have more than 4 devices in your home that you want to connect to the router, then you could connect an ethernet switch to one of those router ethernet ports to allow even more devices to get direct ethernet connections to that router (and that modem access to Internet Land).