Cave story could be seen as breaking ground for popularizing not necessarily a 'style' but more of a mindset. Older games, including indie games, seemed to be fighting a battle to try to express a lot in pixel art, and came up with varying degrees of failure. Cave Story embraced simplicity to make the artwork manageable for a lone developer, and what was taken from this by the community was a utilitarian and minimalist view of pixel art, one that shaped a lot of indie games in the following years and ultimately inspired design choices seen in Sword & Sworcery EP. If you read interviews
with Superbrothers, you'll find a large inspiration for the visual style that they had been developing for over half a decade prior to the release of Sword and Sworcery EP were the same things that Amaya tried to do with Cave Story.
I'm not saying it was the first to choose a style like this, but it was definitely the most notable departure from the norm that I can think of. Take note that Cave Story began development in 1999
, it's safe to say that Amaya's decision to be inspired by retro graphics like the original super mario was way ahead of his time, when the games industry at large was focusing on prerendered graphics and 3D.
While that's a level of granularity that might not be worth getting into, I definitely feel Cave Story (2004
) deserves an entry on the timeline.