Ok looking at the little box it uses, looks like it takes the spdif optical signal from the PS4 and just sends it wirelessly to the headphones. It doesn't override the PS4's DAC.
It would appear the box isn't compatible with the PS4 via USB so you would need to use an external USB DAC and plug its line out into the Steelseries' line in.
Its kind of tricky to find compatible DACs for PS4 but it seems most plug and play ones (don't require additional driver) should work.
I think one thing to try before you go shopping for one is to mess with your optical audio settings on the PS4 itself. If you're using spdif and stereo setup like headphones, using the audio format priority setting of LPCM will send uncompressed stereo audio which would tax the PS4's CPU. Now, if that is the setting you've been using, try using bitstream (DTS) compressed audio, and see if the audio problems continue.
Edit:
Actually, the website says you can in fact use USB. Try that first. You would need to use the optional power cable with this method. You would use LPCM audio with this.