Yes they do, unfortunately. And there are recently discovered cases of chronic wasting disease (CWD) in elk, deer and moose worldwide. I hope it doesn't pass to humans. For the time being I'll refrain from eating game.
I would be more worried about beef. There has been no evidence of CWD jumping to humans, but there has been for BSE.
Also, do you have a link for the distribution? My understanding is that it is spread over a large geographic area, but that it's found in smaller clumps.
There are several maps and studies, depending on which country you're interested in. The best one that I've found was for Norway. Needless to say, it's spreading over an increasingly larger area every year.
Yes, BSE is also worrying, but beef that you buy at supermarkets is also checked more thoroughly compared to game meat. I'd worry more about restaurants and their suppliers.
