I am assuming they give the wine to workers that do a good job or those they have meetings with. As for why it can only be her is partly by pin pointing it to be hers. After all there every few wine made that year so it became exclusive for royal to use. It was explained that the emperor hated that kind of wine and they made a lie to say that the other express doesn't have any. That would mean that the only people in the whole kingdom who would own that wine would be just that empress and her son.
As to why it incriminates her more, is that it was recently opened. So that would mean that someone just had a meeting with the doctor moments before he poisoned the king. It honestly could be just a coincidence but it raises dought as to why the empress would need of the doctor at all especially right before he tried to kill the king. Even today with crimes, even a bit of incriminating evidence can get someone questioned. So I assume that the wine and the meeting the empress had plus the doctor saying it was her is what helped arrest her.
I hope this makes sense.
I didn't get what was it about the wine and how did it showed that the empress was arrested?