It works because whenever you make a payment the merchant sends MasterCard certain data, which MasterCard then sends Monzo, as part of the payment authorisation process.
One of those bits of data is the MCC (merchant category code) & all merchants, whether online or on the highstreet should (the system’s not 100% reliable) have an MCC that identifies them as a betting shop. Monzo can choose to decline payments to merchants which have certain MCCs.
This system is also used for corporate expense cards, for example, to help stop employees expensing things that they shouldn’t..