Cheney is surrounded by law officers 24-7, so there is zero chance he could drink and any of them would allow him to then handle a gun.
Thank you.
In his own words he did drink at lunch, so this is a moot point.
Better question/point would be how much time passed from when he drank till they started hunting again. Sounded like it was a while. Can't say as I wouldn't do the same on a sweet hunting ranch like that, but as many of us know it's still pretty dumb to have even one and then go shooting.
Past that, and barring any further drama, this is all a bit of a non-story story.