Bottom line is that you must have an HDMI input on your TV or Receiver. There are AV converters that allow you to connect HDMI sources to older analog devices using component cables. Of course, this means that your TV must have component video inputs.
You're right about the DirectTV DVR. It is output only. How you set up the ATV depends on your tv inputs and your older receiver inputs. You don't need an HDMI receiver if your tv has HDMI inputs, you would just need to figure out how to send audio to the receiver.
If you have an HDMI TV and a receiver with optical audio input, the ATV has a digital optical audio output. Connect ATV to TV via HDMI and ATV audio to receiver via optical cable.
If you have an HDMI TV with RCA audio outputs and an available RCA input in your receiver, connect the ATV to your tv via HDMI and then run audio out of TV "audio out" to the available receiver RCA audio "input". You may have to turn the volume down on the tv while listening to the receiver. This depends on how your tv handles sending audio out from an HDMI input. Some TV's have a feature that let's you mute the internal speakers.
I more concise remedy can be provided with more info about the inputs and outputs available on your tv and receiver.
