In particular, no, most people don't care about the accuracy of medieval pigs. In general though, realism is often important for its consistency and for the ability to link the game to outside resources.

A lot of writers, artists, worldbuilders, etc like to incorporate realism into their creations, but in my opinion the more important part is having consistent systems, and realism is just used as a shortcut to consistency. Obviously a fantasy story with dragons isn't realistic, nor is a sci-fi story with superluminal starships. But what good media does is ensure that what it shows is consistent, that there's no magic or technology that would break the system or create a plot hole, and that in general what you see on the screen or read on the page is the natural result of background systems. Like, the article says that mature male pigs were rarely found in pens in the village; this is the result of the background system of how pigs are farmed. If you're watching a movie or playing a game and see a pigpen in a village and it only has sows and piglets (assuming you can somehow tell male and female pigs apart), then that hints that the creator knows about those background systems and takes them into account in their works.

The second reason that realism is values, especially in games, is that it means that you can use your existing knowledge of real systems in game, and similarly use your game knowledge to better understand real systems. For example, I play a game called Hell Let Loose, a WWII multiplayer shooter whose maps are created with period maps and aerial footage. Going into the game for the first time, I may not know how the game plays or what its specific mechanics are, but I know that, for example, Pavlov's House is going to be a great defensive position. Similarly, when I watch a WWII documentary or show like Band of Brothers, I can see where they're fighting and recognize the location from my experience on the Normandy maps, and think about how difficult it is to take those objectives in the game. Of course, the game is a game, its systems aren't directly transferable to real life, and playing a game isn't nearly as difficult as real life would be, but because the core of the game system and the real system are the same, the game helps me better appreciate what the real soldiers went through.

In my opinion, people fundamentally like making connections between things they know. Novelty is appreciated as a way to form new connections. If people can look at a piece of media and make connections to it, they'll enjoy it more. Similarly, if people can look at a piece of media and make connections within that media, making predictions as to what's going to happen, or connecting the actions of two characters when the media doesn't make an explicit connection, then they'll enjoy it more as well. These connections are facilitated by consistency and accurately following the rules of the systems in play. If the show is realistic, then people have an intuitive better understanding of those systems and can make more connections, increasing their enjoyment of the piece. Realism isn't required, but it offers more potential connections and helps ensure the background systems are being followed.