Warhammer 40,000 has a small library of rulebooks, rules supplements, codex sourcebooks, codex supplements, alternate army lists, Imperial Armour collections, Chapter Approved collections, etc, etc. And that's just the latest edition.
Fiction set in the universe expects you to be familiar with pretty much all of the general background, as well as the appearance and abilities of anything with a codex entry. So instead of a monster description you get something like "oh no, a Lictor!"
The metaplot in the old World of Darkness. You can play the roleplaying game without the metaplot, but the game writers scattered the metaplot and canon character background stories across various rule supplements, novels set within specific gamelines, crossover novels between the different gamelines, and computer games. Vampire: The Masquerade especially had the whole series of "clan novels" towards the End of the World metaplot. The final supplements that detailed the final fate of the various races and factions (or at least gave lazy Write Your Own Ending options to chose from) still sucked. Other people found it completely awesome, though.
This was especially egregious with later books, in particular the later Changing Breeds books. The Nagah (Were-snake) tribe book is the only book that ties Hunter: The Reckoning into the rest of the Werewolf/Vampire line, and does this with a single paragraph. Turns out that Hunters are Gaia's last-ditch attempt at saving herself, since all her other children have utterly failed in the task.
Collectible Card Games do this to an extent. Sure, there are starter sets with rulebooks but if you are simply buying packs of cards you will have to go online to read up on how to play. Even if you buy the starter set you will still have to read up on the 'advanced rules' on the official site.
This also applies to such games that try to incorporate an actual storyline spanning one or more sets due to the inherent 'snapshot' nature of card art and flavor text. Magic is one fairly prominent example — it's not hard to get a general idea of what's going on in a given setting from just the cards, but those still leave plenty of blanks to be filled in via the novels or articles on WotC's website.
Before the Magic novels, players pretty much put the storyline together based on the snippets of flavor text on the cards (eg. Ice Age and Antiquities).
Legend of the Five Rings is also notorious for this, with every expansion "main pack" containing different snippets of storyline depending on the faction of the said expansion pack. Furthermore, there are also novels, short stories published on the website, as well as the little snippets on the cards themselves.
Also applied to some art, with two or three cards forming diptychs and triptychs, or displaying some sort of event in snapshots (as in Iaijutsu Challenge, Iaijutsu Duel, and Kharmic Strike.)
Eberron. Eberron Eberron Eberron Eberron Eberron. 90% of the details and Dungeons & Dragons statlines can be found in the extra sourcebooks like The Forge of War and Faiths of Eberron.
True of pretty much any D&D setting across the history of the game (and many, many RPGs aside from D&D, as well). The core setting books/box sets are there to provide just enough information to start your own campaign in that setting if you want to fill in the little details yourself. However, the extra books are there to fill in all the blanks for those who want the "official word," and for the development of the metaplot. In other words, it's a common scheme by RPG publishers to get you to buy more books. That, and highly detailing a whole world would make many books into weighty $100+ tomes — like Monte Cook's Ptolus, which clocks in at 672 pages detailing a single large city.
Shadowrun, especially in the first through third editions, put nothing more than a timeline in the core books, but had a vast multi-leveled metaplot through the published adventures and, most well-known, the in-character "comments" section of the sourcebooks. Each story arc of the story of the metaplot was hinted in previous books, from the bugs to the Otaku.
In the board game Talisman, the entire story of how the victory causing Crown of Command got to be where it was and why the world is in its current state is in the manual, and easily ignorable for players who just want to roll dice and acquire treasure.
The point to having such a long backstory was three-fold: 1: to ensure the GM would never actually read it and 2: Since he would never read it except for in excerpts i pointed out to justify things, I could re-write and change things around completely at random without anyone noticing and MOST IMPORTANTLY 3: Convince everyone that I was serious about this character, and that it wasn't simply the game wrecking bullshit that it was. Dickish yes, but he really did have it coming.
Anima: Beyond Fantasy is another good example. The game has a fairly rich setting that, however, is scattered among a RPG (and its manuals), a miniatures game (better said, its manual), several card games, and a videogame. No doubt Crack Is Cheaper.
The Yu-Gi-Oh! card game has (or rather, had) a somewhat extensive metaplot if you paid attention to the flavor text of some of the cards, though some of it was apparent in the artwork. Since cards only have either flavor text or effect text, the sudden drop off of monsters with no effects caused this to all but disappear. "Master guides" explaining the background of the card game's universe were released, explaining things that the cards didn't get a chance to. Newer strategies involving Normal monsters means that Konami is producing more new cards with flavor text, so this might turn around.
BattleTech. If you want to understand why giant robots are blasting the crap out of each other, to say nothing about picking out which faction is the "good" one, you need to delve into the almost excessive amount of supplemental material.
The background material for Star Realms and its fantasy counterpart Hero Realms isn't included in the game manuals, but is accessible on the publisher's official sites.
The names of the Hasbro Beyblade Burst Forge Discs and Performance Tips are not mentioned on the packaging or in the instructions, which just uses their part numbers. However, they are given their proper names in the app/mobile game, viewable while editing a Beyblade.