Note that they actually did set the minimum requirement to "a PC video card from 10 years back": http://store.steampowered.com/app/584400/Sonic_Mania/

Memory bandwidth is the main concern when blitting several layers of pixels 1:1, unless you have some kind of crafty system in place for avoiding overdraw. Although Sonic Mania seems to genuinely use a 320x240-ish internal framebuffer, so my wild guess is that the bottlenecks relate to scaling and post-processing, or possibly some funky driver use causing sync issues.