Nope that adapter won't work. It requires an analog DVI signal (essentially old style VGA over DVI). HDMI sources only output digital, so the DVI only has the digital signal on it, which prevents it from working with that adapter. The only solution is to use the component inputs on the Z10000 if you want to be able to adjust brightness and contrast. For DVI it is fixed. If you search back several years ago you will find a lengthy thread that complains about this.
In my case I'm connecting an HTPC to the DVI input, and I'm able to adjust brightness and contrast on the PC side through the display adapter driver. Most other DVI/HDMI sources like cable boxes don't have a way to do this, so you are stuck.
This is one of the very few complaints I have had with the Z10000 in 4 years of ownership. The others being the loud fan and a hissing sound that eventually went away.
I'm just about to upgrade to a new projector...