Does anyone know what this art style is called? I need to know

I could be wrong, but I'm pretty sure it's just "pixel art".

The occurence of sprites appearing more frequently on a google search has to do with sprites being far more commonplace (and easier to create) than full pieces like this.

The grain/dots you're referring to are just a popular method of communicating shading at the time, so may be better off referring to the era these games are made in.

>>273887
Perhaps this is what you're looking for, OP:
https://en.wikipedia.org/wiki/Dither

I'm far from an expert, but this heavily dithered style of art was used to squeeze as much color as possible out of older consoles at the time. This is especially prominent in PC-98 games due to its 16(?) color limit, and some of the best examples on the system are absolutely beautiful if you ask me.

If you want to learn more I suggest reading up on dithering in games. "PC-98 dithering" might be a good Google search to start with. Otherwise you could lurk around /vr/ until a PC-98 thread pops up. The people in those threads are (usually) a friendly bunch and would probably happily explain the more technical aspects of it, and they at the very least know far more than me.

Hope I could lead you in the right direction OP.