So the SNES had a really, really weak processor which meant if you did anything that needed to do special math, the processor couldn't keep up.
Here's an example from X2 -- to be able to draw Sigma's head as a polygon wireframe like this, the SNES needs to do lots of trig math for the rotations and perspective correction. The regular SNES has some techniques for fast rotations of sprites in 2D ("Mode 7") but can't do the same thing for points in 3D space like this polygon mesh. And at 3.5 Mhz the processor doesn't have a lot of juice to spare to do the math!
Capcom made their own processor called the CX4 to do this stuff, and it's only used in X2 and X3, nothing else! The upside is that those games can do some cool unique stuff. The downside is that you can't rely on the emulator to have implemented it for other stuff.
Here's a list of the main SNES chips and whether we think they're implemented:
CX4: Used for polygons in Mega Man X2 and X3 [neither in SNES classic]
DSP-1: Used for sprite rotation in Mario Kart and Pilotwings [Mario Kart is in SNES classic]
SA1: Used for a bunch of math and drawing stuff in Super Mario RPG, Kirby Super Star, Kirby's Dream Land 3, and a bunch of other late release games [Super Mario RPG and Kirby Super Star are in SNES classic]
Super FX: Used for polygons in Star Fox and Yoshi's Island [both in SNES Classic] -- and in addition Star Fox 2 uses an upgraded version of the Super FX chip, so that's also supported
S-DD1: Used to decompress compressed data in a handful of huge late release games like Star Ocean and Street Fighter Alpha 2 [neither in SNES classic]
There are a few other chips used for random minor games and a few Japan-only chips, but those are the main ones for games you would have heard of. So the good thing is that the four most common chips are implemented in the emulator for sure. We're just not sure about CX4 or S-DD1.