Yes, by the older way of saying "asilo", by more comtemporary wording "casa de repouso/lar de idosos/lar para idosos".
There is another meaning to nursing home
as well, that is "casa de convalescença/hospital de convalescença." (it seems like being specially used when referring to a care facility for the elderly, but sometimes it means "clinic".)http://www.thesaurus.com/browse/nursing%20home
As the sentence mentions "residents", it suggests (to my thinking) that the meaning is of "casa de repouso/lar de idosos/lar para idosos".