How people spend their free time is a cultural element we can develop. If they are out adventuring and saving the world, they may lament not enjoying their usual pastimes, or find ways to inject them into their adventuring life. Using the United States as an example, men stereotypically watch a lot of sports on TV and may attend sporting events in person. Women shop, talk about their feelings, and gossip (or so men believe). Those with dogs must walk them or take them to the park. Both might take fitness classes or enjoy exercise like swimming, jogging, or biking, to name a few. Some people enjoy cooking while others enjoy eating out and can’t cook a thing. There are countless activities like fishing, off-roading, or travel.
We don’t necessarily need to invent pastimes for our world. Many of those just listed are universal, as are countless others. However, we can put a new spin on them. If we have a pet dragon, that presumably comes with different responsibilities than a dog. Decide what they are; this can be used on multiple worlds, with some minor variations. If hunting is a pastime and we’ve invented new animals, we can decide how challenging each animal is and what trophy typically results. New plants and animals may impact cooking (such as very long times at a low simmer to make something edible), but this is the sort of thing we can invent on the fly. Any plants, animals, magic, or technology that are involved in a pastime gives us leeway to decide how it influences that hobby.
It’s recommended to create a handful of activities for a novel-length work, less for something shorter, more for a longer work. With a novel, one or two can be shown during a scene, such as characters hunting or playing a game of cards or dice during an important conversation. The others can be mentioned in passing; a character can lament not doing one or mock another for their hobby. Two people can look forward to doing something upon arrival at a destination known for that pastime (or not). A character can be made to feel like they don’t measure up because they spend too much time on a hobby. These briefly mentioned ideas don’t need long explanations about rules or anything else. Consider this example:
Kier remarked, “I can hardly wait to reach Illiandor and play valends with someone who doesn’t lose within minutes.” He smirked at those around him.
His companions rolled their eyes and one replied, “If you spent half as much time on swordplay as on card games, we wouldn’t have to save you every other encounter.”
“Right.” Antar flashed a grin. “Maybe next time we’ll just let you be killed and take back your winnings that way.”
The captain strode in. “No time for gambling ashore boys. We’ve a hanging to stop!”
What may take longer is the invention of games or sports, if the details are to be shown. Smart world builders will take existing games and modify or combine them. This is easier when the existing Earth game features an animal and we’re substituting one we’ve invented. It’s differing abilities might mean new rules, especially if it has abilities that create unique advantages; we only need to decide what those are and place restrictions on whether they can be used at all, under what conditions, or how frequently. Most Earth sports involving animals feature horses, elephants, or camels, as these are the few ridable options. Some games involve animals fighting each other, but there are likely few rules in such a case because animals, by their nature, are not going to understand or obey them, unless our invented ones are smarter.
Our invented species may also have attributes that are forbidden or restricted in use. Perhaps a team can only have one elf, for example, due to their skills. Maybe dwarves aren’t allowed at all because they can’t compete due to height. We can just decide how the game is played (by humans) and consider the pros and cons of others and what problems their attributes cause; these problems will result in rules to deal with them. All of this applies more to sports than something like card games, as physical attributes greatly impact the former but mental ones the latter.