Sounds like what we term "blood shot" in the meat industry. Packers have told me that this can happen if the animal gets agitated prior to slaughter, I also feel it can happen to wild animals that take longer than normal to expire.
    Basically it is ruptured blood vessels. It doesn't hurt anything but the appearance.
    I cut a beef round into round steak years ago that had the same appearance throughout all the steak. I figured what caused it when a few BB's fell out of the steaks as I was trimming them. Glad we don't shoot deer with duck loads!

Dave