Cheese is OK as long as you have no casein allergies, which you probably don't.
Wine is low on the list of things to eliminate. This article painted a picture of some wacky lifestyle built around a paleo canon. I suppose with this sort of thing a lunatic fringe is inevitable. That stuff in the article about giving blood was just nonsense.
It's really just a short list of diet recommendations. Eliminate sugars & sweeteners and cut grain & potato products as low as feasible and you're doing 90% of it and getting 90% of the benefit.
Starches mixed with proteins (animal proteins in particular) stimulate the stomach to over-produce digestive acids which strain it, and as a result bile needs to be produced to neutralize the acids which strains the small intestine - it often results in very little nutrition actually being absorbed from the food because the acids produced for the two different types combine into an acid that doesn't digest either starches or protein very well.
Meat and Potato diets are highly stressful on the body, also keep in mind that the fasting aspect of this "paleo" diet is very important, without the fasting, your colon won't have enough time to eliminate all of it and it can end up compacted in the colon.
Consistent and high animal protein diets are unhealthy, but animal protein diets spaced with fasting and vegetables (fibers and nutrients) are great for the body.