Hi,
Could be due to DRM (Digital Rights Management) in iTunes. Please note: HDMI cables normally carry HDCP (High-bandwidth Digital Content Protection) signals. DRM and HDCP will work together to stop you to use HDMI to play on external device(s). Many tricks and hacks around which allow you to remove DRM. Due to HP policy: do not post hacks on this forum therefore I can't tell you how. Just Google and you can find one.
Good luck.