Could you please share what sort of rules system powers this game?

Of course :).

Townsfolks, the heroes of the game, are described by narrative Traits, the most important of them being the Concept Trait (like Pious Farmer, Disillusioned Conestable and so on), a series of Assets (think of them like iconic pieces of equipments, or connections, like My Father's Bible, Library of Ancient Books, Muckracker Friend at New Your).

The character is completed by 2 numerical values: Endurance (covering both physical and mental health), and Luck (useful to reroll).

For most of the time, play unfolds as a natural conversation: players describe their Townsfolk’s actions, and the Chronicler narrates the world’s responses.

No dice are needed unless the Townsfolk face a risky situation—known as a Threat. 

When confronting a Threat, assemble a dice pool as follows:

+1 die if an ordinary person could reasonably overcome the Threat.

+1 die if one or more of the Townsfolk’s Traits are relevant.

+1 die if one or more Assets provide a clear advantage.

+1 die if a companion provides substantial aid (note: if the roll fails, both suffer the consequences).

Roll all dice in the pool and consider only the highest single value. Then consult the Threats Table.

If the Highest Value you rolled is...

1: Critical Failure - You suffer the consequences of the Threat and a Setback — but regain 1 Luck.

2-3 Failure - You suffer the consequences of the Threat.

4 - Partial Success You overcome the Threat, but suffer a Setback.

5 Success : You overcome the Threat.

6+ Critical Success: You overcome the Threat and gain a Breakthrough.

Hope it helps!