It would have been helpful if the OP had mentioned that the sentence comes, as Google reveals, from the Wikipedia page about John Houghton (c. 1486 – 4 May 1535), a Carthusian hermit and Catholic priest. The 'house' here is the London Charterhouse, which was, prior to the reign of Henry VIII, a Roman Catholic monastery belonging to the Carthusian Order.
Regarding the usage of 'house', this word can be used for many types of building, not just a family domestic residence.
noun (PUBLIC BUILDING)
a building or part of a building that is used for a special purpose
A house can also be a building or part of a building which is used by
House (Cambridge Dictionary)