To be frank I've never paid attention in-game so I don't know if the mechanics coded within the game deal the extra damage. However, I'd like to know if they're coded within the damage system or not.
I'd really appreciate if someone can show me some proof as to whether or not these abilities actually do the extra damage. This applies to both battle simulators as well as the games themselves, but obviously its much easier to show me a reply from the former.
inb4 Hidden Abilities are better. Yes. I know. I'm curios.
Yes they are. When battling with an ability like this in Pokemon Showdown, it will tell you the increase based on what ability you have.
This link will give you a picture proof of the increase of damage. I've tried it, and the increase of damage is significantly different, and the makers both in Pokemon Showdown and the actual Role-Playing do factor this into the damage system.
Hope I helped! :)