One Xbox and Wii U for sure:
NO NO sound or Astro trick card required!
Just a small adapter to 7; redirect = true & ref_ = oh_aui_detailpage_o03_s01
+ Adapter for this XB1; qid = 1420757767 & sr = 8-1 & keywords = + adapter + headset + xbox one
I use it on Xbox One, Wii U and PC Gamer (Asus ROG end 2014) equipped with a good sound card
On PS4 I think it's the same principle)
The Astro or external sound card are just amps, nothing more!
Regarding the headset nothing to say it is perfect, but that all the world knows!