Animateness-neutral "its"

This is not a singular they, as your tags imply it might be, but a plural they. In modern American English, we usually treat collective nouns as singular. "The company puts out a press release most weeks, but it skipped this week."

In the usage you quote (and sometimes in modern Commonwealth English), the collective noun is being treated as a group of people. "The company put out a press release most weeks, but they skipped this week."

The quoted sentence is using "House of Representatives" to mean members of that body. So the plural pronoun is perfectly appropriate, 232 years ago and now.