I'm raising this from the dead.
I ran into this problem where I can get the sound in OBS, but I cannot get live sound to my headset. As you know picture and sound through a capture card is delayed and this will not suffice for when you are playing the game. Upon extensive research I have found a few options.
First off the problem is the PS4 will only output audio using one method. So if it is feeding sound out using HDMI you will not get sound in your head set and vice versa. There are two work arounds that will require purchases.
Option 1: You can get an hdmi converter. So you plug the hdmi cable coming out of you capture card into it and from there the monitor. This should allow you to connect audio using a 3.5mm audio cable to you headphones. This method may also require that you get a component audio cable.
Option 2: If your HDMI cable is running to a TV or monitor with an audio out port simply plug a 3.5mm audio cable into it and to your headphones.
Here are some links for the items that should help.
Component to 3.5mm Audio cable
http://www.amazon.com/3-5mm-Stereo-...1414530970&sr=1-3&keywords=component+to+3.5mm
For the Converter its hard to come up with a recommendation because I do not know your setup. If you can use an AGP connection it will be much easier and cheaper. Here is one with an HDMI out with audio components
http://www.amazon.com/IMAGE®-SPDIF-...id=1414531021&sr=1-13&keywords=hdmi+converter
Here is a standard 3.5mm audio cable just in case
http://www.amazon.com/Mediabridge-3...=1414531276&sr=1-1&keywords=3.5mm+audio+cable
I hope this helps.