Chemistry - If I were to create a fictional way to obtain elements from Granite, what would be a good approach?

First, some specific points:

For this question I'm focusing on a way to decompose granite into useful substances. In reality, thinking in industrial scale, this probably is never done, because of the costs I assume are involved and the return.

It's not only the cost. It's about having huge amounts of waste. You were mentioning Rb and Cs in your question. An average granite will have ppm (parts per million) amounts of Rb and Cs in the rock. Let's say you want to produce 1 kg of Rb, from a rock that has 50 ppm of Rb. The same rock will have, let's say 65% of SiO2. You will end up with 13,000 kg of SiO2 for each 1 kg of Rb!

Granite is also rich in Orthoclase feldspar...I don't know the structure of this species. It's probably an oxide, but unlike SiO2 it probably has some weird bonds going on.

It is a silicate. The metals (cations) in there are ionically bonded to silicate anionic groups (which themselves are ~covalent) such as [SiO4]4−, [Si2O7]6−, etc.

So my question is, what would be a lightly realistic approach to obtain usable compounds from granite?

No. See below.

I'm sure real techniques do not exist, but what about science-fictional approaches?

Real techniques do exist, it's just pointless do do them. You ask about science fiction, but in the beginning of your question you mentioned that your mod "focus on adding realistic chemistry to the game".

Second, a detailed answer:

It is not feasible to produce those elements just from a granite (or a diorite or andesite or any other "conventional" rock). Producing a commodity has several parts to it which determines whether we should do it or not. Since you do not actually care about costs, it may seem ok. But there are also two other important things: effort and waste (as mentioned above). Producing 1 kg of Rb from a rock that has 50 ppm (if you're lucky) requires mining 20000 kg. This is something that's extremely hard and time consuming unless you have the machines for that. Also, think about what you're going to do with the waste rock (13000 kg of SiO2 for example).

Even if somehow you managed to do it, and you have some magic processes that can extract the Rb with little effort out of the rock, you will probably want to do it for every other element in the periodic table. Then it becomes a huge effort. Think about the environmental impacts of digging out a mountain and then building pools of enzymes to digest the thing, and let's not forget the noise and pollution (and energy requirements) made by the machines that grind the rock to powder. Granite is a hard rock, you know?

This is why we extract mineral commodities from ore deposits. Luckily, mother nature provided us with certain types of rocks that are enriched in an element or a group of elements. Then, if we want to produce 1 kg of Rb, we don't have to mine 20000 kg of rock, we only need to mine 200 kg of rock or less.

Another question, why do you need Rb for, or any other metal? Do people mine stuff just for fun or do they actually need this for something, in-game? I would suggest that you come up with a list of elements that may be useful for someone in the game, and then think of an ore deposit that may hold this. For example, granites occasionally have certain "segregations" called pegmatites. These rocks are heavily enriched in certain elements, such as Li, Cs, the lanthanides, Be, Sn, etc. You can make up spots of pegmatite in your granite world so people can mine that. As a bonus, pegmatites usually host pretty crystals of stuff.

Once you come up with a list of elements, you might want to ask the next questions in the Earth Science SE, not here.