"Spatial" is just Apple branding for Atmos. Any AVR that can decode Atmos can play it. Though the marketing materials all focus on headphones because that's what Apple is selling.
I "think" Spatial Audio refers to the Apple audio process that accommodates "head tracking" with specific devices (headphones and IEMs) that are compatible with that technology. When you turn your head, the 3D sound image remains stable in its location around you, not moving with your head movement (supposedly.) I believe that Dolby Atmos and/or Spatial Audio files will still work as intended with any stereo headphones, but the head movement tracking feature won't. Someone please correct me if I'm wrong.
In my opinion, Apple and Dolby Labs have done a distinctively poor job of explaining all this to consumers, like, not bothering to try to explain it at all. A similar situation exists with trying to hear a genuine HiRes audio signal through an Apple device with an outboard DAC. To do that from my iOS devices I have to assemble an unruly mess of wires and adapters to make it work. Not that I ended up caring about any supposed "improvements," anyway.