Ok, here comes the chemistry lesson.
Clays are aluminosilicates. Think of it as sandwich (double, triple, quadrupl or more decker sandwich). Bread slices are silicate layers, mayo is aluminum oxide layer. They are bonded together. (spread mayo on your bread and try to take it ALL off, virtually impossible).
Ok, now the sandwich filling (meat) are usually ions (sodium, potassium, calcium, magnesium even other metals, lots of research being done in using clays to bind (heavy) metals like lead, cadmium, etc..)
These don't come out easily (mayo keeps it sticky), but if you pull on the side, it slips out. The clay can actually (in the fining process) affect the type of ions (electrolyte) in the wine, but will not had more (must maintain electrical charge balance)
Now, clays actually swell in water (put your bread in water, never mind consistency, but it gets bigger)
Back to the sandwich. If the spacing between your slices of bread is wider, you can slip in stuff without taking the sandwich apart (slip in a pickle slice).
This is how tannins get small ions or molecules get into the clay.
Tannins are fairly large molecules, and would not fit in between the clay layer (like trying to put a whole turkey in between two slices of bread).
Back to the fact that clays swell in water, and become sticky mushy (like wet bread).
Throw dry pieces of bread on the turkey, nothing happens. Throw slices of bread that soak in water, you can probably build up a good layer of soggy bread on the turkey.
That's what fining is. The clay stick to the tannins, and has the clay is precipatating/depositing in the bottom, it drags along the tannins.
Why some tannins stay in the wine, throw wet bread on a quail, throw wet bread on the turkey. Pick but poultry up and shake lightly a bit. Probably all the bread (even wet) on the quail fell off. still some left on the turkey.
The clay just doesn't well enough on the smaller tannin molecules to pull all of them out of solution.
To make things even more confusing, different types of clays behave differently (different types of bread are more stiff like rye, vs. white bread), and are different size (small bread bun, to a whole pumpernickel loaf).
Sorry about the sandwich analogy, but I'm having lunch.
To wrap things up. Fired clay, actually binds (forms chemical bonds) between the small clay powder to form a whole solid mass, your goblet.
As for the earthyness, those are probably minerals leaching out. The goblet would not have any appreciable effect on the tannins levels except for the small amount that might be adsorbed on the surface of the fired clay. (unglazed fired clay surface to use an analogy, would be a piece of toast. Even wet, meat wouldn't stick much to the surface).
Hopes this helps. I've tried to dumb it down as much as possible. Not CHEM 101, more like CHEM 001