Maybe not what you’re looking for exactly, but you might find this article relevant and interesting: https://kotaku.com/the-decade-in-five-games-1840394803
I feel like Prince of Persia: Sands of Time changed mainstream platforming forever. As one thread of progression, you might check out PoP: SoT (maybe you already have since it was PS2 era), Uncharted 2, and then maybe the Tomb Raider reboot? That’s particularly interesting because the original Tomb Raider was one of the pioneers of 3D platforming, and the reboot basically just follows suit with other modern AAA games, which were no doubt inspired by the original Tomb Raider. That said, I think that style of platforming is on the decline in the last couple years as Souls-likes gradually inherit the earth.
I definitely agree Demon’s and/or Dark Souls and/or Bloodborne should be on the syllabus. Or skip straight to the best of From Software’s “death games,” which is quite obviously Sekiro imo. Surely some of the most influential games of the last decade, for better or worse. Not sure if sequence/chronology is that important here; I feel like basically all the critical concepts were established in Demon’s Souls in 2009 and from there it was just polish and gradually backing off some of the more mean-spirited elements (making checkpoints more lenient, etc).
Speaking of critical concepts, Demon’s Souls et al lifted many of their mechanics from Monster Hunter, and that’s unquestionably one of the most influential series in Japan of the last fifteen years. I’d maybe start with MH: Freedom Unite on PSP (available on PSN for Vita and also iOS) and then check out MH4Ultimate on 3DS and MH: World on modern systems if you want to see the evolution.
Probably worth checking out some of the influential indies: Braid> Fez>Meatboy>Hotline Miami>Gone Home>Papers Please. (Without looking up dates, I think that’s more or less listed sequentially, but I guess those games don’t have a lot in common other than being indie and relatively high-profile/award-winning.)
I think most modern open-world games are descendants of Grand Theft Auto III. You could got GTA III/IV/V, and then any random Ubisoft map game (Assassin’s Creed IV: Black Flag is the pirate one and therefore the best one), and then maybe Horizon: Zero Dawn, which is very very polished, and/or Witcher 3, which is very very Polish (also hugely popular).