I'll state an old classic that is seen as a genre defining game because it is: Myst. Yes, it redefined the genre... in ways I fucking hated and that the adventure game genre took decades to fully recover from. It was a pompous mess in its presentation and was the worst kind of "doing action does vague thing or nothing at all, where is your hint book" puzzle gameplay wrapped in graphical hype which ages pretty poorly as far as appeal qualities go.
So many adventure games tried to be Myst afterward that the sheer budgetary costs and redundancy of the also-rans crashed the adventure game genre for years.
I almost mentioned not liking Halo from the very first game when it first came out, finding it clunky and chunky and having controls that made me feel like an armed refrigerator with tank treads equipped with a camera and the story being both flag-humping hoo-rah apologia and a pretentious mess that was only wearing the peeled off skin of the Marathon series, but I'd get soooo much shit so I waited for someone to say it first.
The lore is pretty vast, but the games don't really explore it all that much. It's more sprinkled in, and mostly told through the books and game extras.
I enjoyed the music and the co-op, but the lore of the game felt very clearly like a "secular US military in space" fighting against inscrutable religious zealots (with an Abrahamic theme) then zombies, which to me feels like Stargate (the show). Idk if that's something that scans, it just popped into my head discussing Stargate and it's cagey relationship with the religious right of the bush era (and some big name culty events like WACO, which I feel like provided some cultural energy to the Brotherhood of Nod)
I have no idea if this will affect your opinion of the series positively or negatively but here's some information that recontextualises the religious themes:
Humanity are actually the descendants of the gods of the Covenant religion, and explicitly hold an honoured place within the philosophy practiced by those gods. The covenant are trying to exterminate humanity because the religious leaders are suppressing this information from the general population and using genocide to keep their secrets.
That and em dollar sign sinking its tentacle into gaming because if it wasn't for Halo 1, the Xbox would've been a complete dud. We live in the timeline where the Dreamcast floundered while the Xbox survived.
In the first game you have the genocidal theocrats trying to wipe out humanity, and you have humanity represented as the roman empire in space. So both sides are basically fascist. And the player character proceeds to accidentally almost wipe out all life in the galaxy by trying to find the biggest gun and use it against the baddies. Cortana has to step in, call you a nincompoop in a bizarrely british accent, and inform you that Halo will wipe out all life in the galaxy. The lesson here is that you should stop and think instead of uncritically participating in the cycle of fascist violence.
In Halo 2, you play as a military leader participating in a theocratic genocide, whose cultural traditions have been turned against your species to turn you into a willing slave of the rule caste who does their dirty work and has no honour so you'll stop asking pesky questions like "Why are we killing the humans". You meet heretics, a light bulb, and a big venus fly trap who slowly deradicalise you, until one day your people are genocided and you team up with the people you oppressed. The lesson here is that you should stop and think instead of uncritically participating in the cycle of fascist violence.
In Halo 3, Earth is invaded and the covenant find a portal to the Ark, through which Cortana says there is a way to beat the Flood. Lord Hood wants to stay at Earth and go down in a blaze of glory, but Master Chief and arbiter who have learned their lessons from the last two games, say they should go through the portal and see what Cortana's big discovery is. The lesson here is that you should stop and think instead of uncritically participating in the cycle of fascist violence.
In Halo ODST it turns out that Huragok are slaves actually and there might be something to be gained by saving them from the covenant instead of killing them like you have been the whole game. The lesson here is that you should stop and think instead of uncritically participating in the cycle of fascist violence.
In Halo Reach, Noble Team try to go down in a blaze of glory defending Reach, but Halsey gives them an AI she says has the secret to winning the war, and it turns out Cortana has the coordinates of Halo. The lesson here is that you should stop and think instead of uncritically participating in the cycle of fascist violence.
In Halo 4, Captain Del Rio doesn't want to risk damaging the Infinity because it's a ginormous phallic substitute for his fragile masculinity. Chief and Cortana have actually been spending their time exploring and studying the lore, and they go rogue and save the world. The lesson here is that you should stop and think instead of uncrtically participating in the cycle of phallic symbols