There was a lot of trouble around the Buckyball magnets a few years ago, with the U.S. CPSC saying that they were unsafe for children because if a child swallowed two, they might attract one another from different locations within the child's digestive system and cause injury. (The manufacturer of Buckyballs was apparently very upset about the outcome.) It's interesting to think that swallowing magnets was seen as a serious threat to human digestive systems, but here is used to protect cows' digestive systems.

Is the difference just in the cows' anatomy and the size of the magnet, so that this magnet is guaranteed to stay in the first stomach and not go any further, while human anatomy doesn't work that way?

It seems like having cows swallow very small magnets (that can advance beyond the first stomach) would also tend to injure them, because those magnets could attract metal objects from one part of the digestive system toward another, as the CPSC feared with the Buckyballs.