I don't think that's true? There's nothing special about Apple's implementation of Dolby Atmos over headphones besides the head tracking bit (and that's not needed for music) that need their headphones. If you set Dolby Atmos to "Always On" in the settings it will give you the Atmos headphones mix regardless of what headphones being used. Airpods and Beats are still just stereo headphones.

Atmos works pretty well over normal stereo headphones and I've used it for years on PC while watching supported Blu-rays.

I'm kinda peeved at Apple's lazy implementation because it's only supported on Apple devices and not devices that support Atmos and work with Apple music like a PC or Samsung Android phone.