There may be limited Anynet+ connectivity with the game console because it doesn't have Anynet+ capabilities. While the hardware is detected or named, that is likely because it can also be used as a video server.

If it doesn't work correctly through a Home Theater, you may try changing the resolution to see if the signal passes through. Otherwise, you can use an optical cable from the game console to the HT system, and connect the video via HDMI directly to the television.