https://www.kickstarter.com/projects/1661802484/hyper-light-...
Those concepts are loosely carried over to modern pixel art. In most cases 256 colors is enough for static pixel art, especially if you avoid gradients (as most artists do).
Or take the Sega Genesis/Mega Drive, a 16-bit console; its colour capabilities didn't give anything close to 2^16 = 65536 on-screen colours. Instead you got a 9-bit palette with only around 64 on-screen colours [2].
[1] https://en.wikipedia.org/wiki/List_of_video_game_console_pal...
[2] https://en.wikipedia.org/wiki/List_of_video_game_console_pal...
There's no such thing as an 8-bit pixel resolution. In fact even amongst the 8-bit consoles, their output resolutions differed: NES: 256x240; Master System: 256x192; Game Gear & Gameboy: 160x144; and the Atari 7800 supported a few different resolutions.