The understanding here is that a house organ is a periodical distributed with 'management' sanction, primarily internally within an organisation (i.e.: in house), as a means of communication.

Two definitions for 'organ'. The first from M-W, the second from AHD:

4. A medium of communication between one person or body and another; as, the secretary of state is the organ of communication between the government and a foreign power; a newspaper is the organ of its editor, or of a party, sect, etc.

4. An instrument or a means of communication, especially a periodical issued by a political party, business firm, or other group

Middle English, from Old French organe and from Old English organe, both from Latin organum, tool, instrument, from Greek organon.