Spoilers ahead: for the puzzle and the movies/games
This post assumes you've already solved the puzzle. It reveals all categories and their connections, and discusses plot details, endings, and spoilers for featured movies/games throughout.
Pokémon White Version 2 makes you enter the Hall of Fame before you can reach its Day Care. Finish the main story first, then start planning Eggs. An impressive amount of professional development for a job that mostly involves leaving two creatures with someone else.
Games: Top Spin · Virtua Tennis 3 · AO Tennis 2 · Tennis Elbow 2013
The original Top Spin arrived on Xbox in 2003. Its later Windows and PlayStation 2 versions have different release histories, but the activity stays comfortably recognisable: singles, doubles and the repeated discovery that the ball has gone somewhere inconvenient.
Virtua Tennis 3, AO Tennis 2 and Tennis Elbow 2013 complete the court. That last title has a small calendar trap: the 2013 game reached Steam in March 2015. A storefront arrival can be later than the game itself. None of that changes the answer, which asks what you spend your time playing rather than which publisher gets the credit.
Games: Driver · True Crime: Streets of LA · True Crime: New York City · Police Quest: In Pursuit of the Death Angel
John Tanner in Driver is an undercover officer infiltrating a criminal organisation. The car-chase presentation makes it easy to remember the driving and forget the job. He belongs with the cops, even when the traffic outside looks unconvinced.
The True Crime pair gives you LAPD detective Nicholas Kang and New York officer Marcus Reed. Police Quest casts you as Sonny Bonds, a fifteen-year veteran whose assignments move from patrol into narcotics and undercover work. Different cities and interfaces, the same playable role. Bonds is also a reminder that this group reaches back to a 1987 adventure game, well before the PS2-era open-world police fantasies.
Games: Pokémon White Version 2 · Dragon Quest Monsters: Joker · Viva Piñata · Dragon Warrior Monsters
The Day Care's two available slots in Unova support compatible Pokémon pairs producing Eggs. In White Version 2, reaching the facility is a postgame requirement. The mechanic belongs in the group even though it isn't waiting for you on the first afternoon.
The Dragon Quest games ask you to think in generations. Dragon Warrior Monsters first released in Japan in 1998, with its Western release following in 2000. Joker calls its successor-producing process synthesis: the resulting monster can inherit skill sets from its parents. An Egg animation isn't the requirement here; combining parents to produce a new creature is.
Viva Piñata wraps its animal-breeding life simulation in a garden full of colourful piñatas. That is an entirely different mood from monster battles, but the offspring link holds. Collecting creatures alone wouldn't earn a place in this row. The family tree has to do some work.
Games: Bulletstorm · Windjammers · Frostpunk · Thunder Force III
Take storm out of Bulletstorm, wind out of Windjammers, frost out of Frostpunk and thunder out of Thunder Force III. Some words are welded into compounds; thunder gets to stand on its own. The spelling supplies the forecast.
Windjammers is the sporting decoy. Its 1994 Neo Geo arcade release belongs to flying-disc competition, not tennis, so it can't fill a spare slot on the court. The wind in its name is much more useful here than the genre.
Frostpunk makes the cold feel like a city-management problem. Bulletstorm and the Genesis shooter Thunder Force III have rather louder priorities. You can know all their mechanics and still miss the row if you keep looking for weather systems instead of weather words.
The breeding group gets the best delayed payoff: four very different games suddenly have a family-planning meeting to attend.
CineLinkr's October 30 puzzle also visits tennis, then trades these police protagonists for witnesses who desperately need protection.