How do I recreate the look of these Gems?
I don't know if someone would call that worn edges but see for yourself. I don't want just the edges to look worn or however that effect is called I want them having that stylized look but still be reflective and realistic.
Texture the gems with handpainted textures with worn edges - to keep it stylized. Also make some roughness texture for the edges so you get more variation in the shader. You can also create multiple materials (for edges, flat pieces,..) and mix them using mask. Go with a glass shader for the surface, you can also mix multiple glass shaders with different IORs to get some fake dispersion effects.
Make the gem fairly transparent and shade the inside of it with volumetric shaders. If the gems will be animated this volumetric part could have some procedural changing clouds inside. Something like this: Volumetric tests
Add a light source of some kind inside the gem. There could be some cloud volumetric emission shader inside. Or add some nice backligh/light-from-bottom etc.
The glow, color correction or some more stylization add in compositor with nodes.
