Use the cable that came with the PS3, attach it to this, and plug headphones into that. Set Video to HDMI and Audio to the third option "Audio Input Connector" or turn on "Audio Multi-Output" to get sound out of the headphones and the TV at the same time.
I tried this solution. I bought the exact cable that you mentioned and tried rigging it to the cable that came with my PS3. I've set the Audio Output Settings to 'Audio Input Connector' and video is set to HDMI, Audio Multi-Output is set to 'On', however I am still not hearing sound out of my headphones.
Anyone have any ideas? I am using Sennheiser HD 598 headphones, but this solution also does not work with a basic set of speakers. This leaves me to doubt that it's the headphones that are the problem.
Nevermind. Turns out the PS3's cable wasn't pushed all the way in. If anyone runs into this problem in the future be sure to simply push the cable into the PS3 until you hear it click.