The phrase their God
can also be translated as their gods.
Since the Israelites were not travelling to Jerusalem for worship, it most likely refers to idolatrous shrines. The poor were unable to pay various fines with their own money, so they paid with wine that was then drunk by the rich.
8 they lay themselves down beside every altar on garments taken in pledge, and in the house of their God they drink the wine of those who have been fined.