I don't think this will work. From what I can see, the only output from this device is via the F-Type coaxial cable. What Jeramiah needs is a device that takes the F-Type input and can strip out the audio so he can connect via stereo RCA jacks to the receiver.
Jeramiah - most folks don't encounter this problem for a couple of reasons. First, just about any late-model TV will have audio out. I'm guessing your set is pretty old if it doesn't have ANY audio out. Second, cable and satellite boxes are generally used to do this very thing.
Does your TV have ANY type of input other than the screw-on F-Type cable connection?
In many areas, cable companies (Comcast, here in Baltimore for example) are starting to require ALL customers (even basic cable subscribers) to upgrade to digital tuner boxes. This sort of device does exactly what you need it to do. Have you checked into whether or not your cable provider has these digital tuners for basic cable service in your area? (They should be available free of charge - they are NOT the same as upgrading to actual digital cable service).
If this isn't an option, have you considered updating your TV? If you can tell us a bit more about the size, environment, etc. we may be able to help you find a relatively affordable solution.