The wild game will become too scarce to feed all the cougars, some cougars will die (and they will definitely reproduce less) and then cougars become less populous. Then the wild game will have room to expand, increasing their numbers, the cougars will have more food to eat and so they will grow in numbers and the prey will therefore decline… and the cycle will repeat itself. That’s how most predator-prey interactions work, on a very simplified level. With regards to your link, anytime you live in close proximity to large wild predators you have to be careful, but I don’t think that humans will become particularly common prey for cougars. Pets on the other hand? Guard your puppies and kitties, definitely.