Dolby licensee here. Pretty much what Fubar said. The concept of using algorithms to create sound vectors from stereophonic sound is several decades old but began in earnest with Qsound in the 1980s.
What makes Atmos different from other perceptual coding systems is that it is more object dependent than channel dependent. That is, while Dolby AC-3 (Dolby Digital), Dolby Surround EX, Dolby TrueHD, etc., are mixed to Left, Center, Right, SurL, SurR, Sur Rear, LFE, etc. channels, Atmos has a concept of sound objects that in the theatrical implementation are dynamically assignable but in the home implementation basically exist as a standard called Dolby MAT, Metadata-enhanced Audio Transmission. Each Dolby Atmos decoder makes adjustments within a defined set of parameters depending on the specific set up, scale and positioning of the speakers in the home theater. If it is a headphone setup, it can use phase shift, time delay, attenuation and other tricks to create the same kind of perceptual cues the brain uses through our two ears to triangulate where sound comes from.
Personally, I think most perceptual 3D DSP today pales in comparison to what Qsound could do back in the day but 1st gen Qsound was bespoke, that is, every element was meticulously engineered and it was insanely expensive, which is why only a handful of first gen mixes exist.
I think of Atmos as less of the DSP trickery than a platform codec that future-proofs against 5.1.4, 7.1.2, 9.2, 14.2 whatever channel configuration you might have, by leveraging the lower cost of hardware processing to partially manage the mix during playback.