|(the key of fancy)|
Monks were literate, had leisure time, and were prone to both gambling and creativity. It is inconceivable that they did not play RPGs. Nonetheless, RPGs written in the monastic context are not forthcoming. Thus, we must make do.
As in our age, the d6 was by far the most common of dice in medieval times. Though in many times and places, dice were forbidden by both common and monastic law, in practice, it was treated much the same as the monastic law against indulgence in food and alcohol.
It seems to me unlikely that there would exist classes as we would think of them (i.e. as a bundle of special rules and bonuses). There would however be specific archetypes accounted for. I'd imagine something like a list of archetypes and descriptions. For instance:
A foolish one who trafficks with fell powers. Despised by the good and christian when recognized, beloved of the pagan and worldly. May tell the future, or ensorcell the unwitting.
A wielder of magic. May cast spells from the list found on page xx a number of times per day equal to their level. Has x hitpoints, and saves as y.
So a sort of class restricted FKR. You are restricted in which things you might be, but those things don't have strictly defined mathematical benefits or universal features.
And speaking of classes, lets talk about what those might be. The fantasy analogue of the middle ages (for fantasy did not truly exist yet) was a mix of oriental, biblical, and classical tropes, filtered through the medieval worldview. You'd have greek gods, heroes, and monsters, except they wear tunics and hose rather than chitons and sandals, and the gods are called fairies or spirits or allegories. King Solomon is there, so are the ruins of babel. There may or may not be demonic antagonists (whether demons were a matter to tell stories and joke about seemed to vary). Dragons are there, but likely compared with other fantastic beasts like lions and giraffes. Magic exists, but is more like medicine or astrology, and also is morally neutral at its very best. Christianity may or may not be depicted. Anachronism is high.
Notes: I am dissatisfied with this as it exists now, but I'm unsure of my expertise, ability, and free time to fix it, so if anyone has any suggestion or edits, feel free to suggest them. As well, if you feel the desire to make your own Game for Monks, I would be ecstatic to see them.