Hmmm - I'm confused, because Air Foil says it will work with Apple TV?
Sorry for any confusion that I may be causing you. AirPlay, the streaming protocol, requires an AirPlay "player" to stream to. This can be an AirPort Express, Apple TV, or an AirPlay-capable receiver like your Yamaha.
iTunes as you already know, uses AirPlay for streaming; so does Airfoil. The only real difference is that "sources" that iTunes uses is restricted to what is available in the iTunes application. Airfoil, on the other hand, is not. That is why it can stream directly from a web browser for Internet radio. Thus, Airfoil, like iTunes, needs an AirPlay "player" to get the audio to the speakers. In your case, the speakers would be connected directly to your receiver. AirPlay would stream the audio to your receiver via an Ethernet connection.
I would connect the ATV to the Yahama by HDMI. Will that work?
Yes ... but again unless you wanted to take advantage of the additional features that the Apple TV would provide you, you would not need it as the AirPlay "player" since your receiver already has one built-in.