Thanks for the helpful photos! It looks to me like the cable box has composite (red/white/yellow) ports that you can use to hook up the the Slingbox using those same color ports. If you need to, you can use the red/blue/green component cables for this connection if you hook those cables up in this manner:
Green cable --> Yellow port
Blue cable --> White port
Red cable --> Red port.
Make sure you use the same color ports on the Slingbox as you do the cable box.
If you choose to run cables from your Slingbox to your TV as well, again, make sure you use the red/white/yellow ports.
Hope this helps!