Was sure i started replying to this a couple of days ago... sorry but I have closed your duplicate topic in the Win8 forum.
1st thing I'll say is the 7.7 patch seems to have caused widespread fps issues, so my gut feel is this is an issue with the game client itself and you'll need to wait for the next patch to see if they fix it...
It IS weird that it is only affecting you when you use HDMI out though.
A few thoughts... what resolutions are each monitor using? The laptop native display is 1080, is the HDMI monitor displaying a higher res?
If you plug in the VGA and run HDMI and VGA only (disable the laptop display) does the issue remain?
When you plug in HDMI, is the sound output changing to the HDMI HD sound device? If so, if you disable the HDMI sound output before plugging in, does the issue remain?
Are you "hot-plugging" the HDMI monitor while the game is running or does it make no difference if you do it before launching the game?
What HW monitoring software do you have?
OpenHardwareMonitor will allow you to track load on GPU and Video RAM when you plug in the HDMI port. Does it spike?