Hello! Dolby Atmos will work with any standard pair of headphones…in fact, that’s what it’s designed for! You don’t need a special sound card on PC or any special hardware on the Xbox One either (As long as you have one of the controllers with a headphone jack).
A lot of the headphones that are sold today as “surround headphones” are actually just stereo headphones using software a la Dolby Atmos. The only multi-driver surround headphone I can think of off the top of my head that’s currently on the consumer market is the Razer Tiamat V2. I would have bought and reviewed one of those by now…but the cable between the headphones and the bass station is hard-wired. So, it would be hard for me to test them in my usual portable coffee shop writing scenario, where I test isolation.
Thanks for reading and for the question! Sorry I got a little long-winded in my reply, haha.