Using HDMI and airplay at same time.

I'm not at all familiar with that particular receiver, but I'm guessing "no" is the answer. Most receivers I know cannot do this even high end models. Only 1 source can be active at a time...you can't separate audio and video. If you had analog connections, you could mix and match some. For example if you had an AppleTV and ran the optical audio to the same receiver input as your cable/satellite box, you could probably switch to that input and tell the receiver to use the optical instead...so it would take video from the HDMI but audio from the optical which would be your AppleTV that you could AirPlay to.

The only other option would be to add speakers to the room and set them up as Zone 2 on the receiver. So you'd play your football game to the "main zone" and then play your airplay/radio/etc on Zone 2 to hear through the extra speakers...it'd only be simple stereo.

Run HDMI from your set-top box directly to the TV, and a digital audio cable (optical or coax, whatever's available at both ends) to your AVR. You'll be switching video using the TV input(s) instead of the AVR in this case, but there's no direct benefit to run a set-top through an AVR at this point. Then you'll be able to switch to an audio source on the AVR while the TV remains on the set-top's input.

And yeah, this used to be a feature of AVR's a long time ago for "FM simulcast" and other purposes, but those features were little-used, and certainly caused confusion if you got into a mode and didn't understand why...

Jeff