You are getting there, but you need to keep reading. Be sure to read pages 19-20 (Weapons policy and University retains right to search persons or property on University property), 28 (policies apply to all buildings operated by the Office of Housing and Residence Life), pages 28-30 (Entry, Search and Confiscation), page 34 (Grounds maintenance for Gonzaga owned off campus residential properties), page 70 (jurisdiction), and pages 71-72 (prohibited conduct).
Then think about how confident you are in your argument that the possession of weapons in a University on or off campus residential facility owned or operated by the Housing Office is permitted under the student code of conduct. Note that your citation as to alcohol use in University-owned off campus residential apartments makes the case that the University can regulate conduct in those properties owned by the University that are 'off-campus'.
When you read the handbook, it is clear that the University considers the student code of conduct to apply to all students, on and off campus, in facilities owned or operated by the University. Now, if these students were living on the economy, in an apartment or house not owned or operated by the University's housing office, I think the University would not have much of a leg to stand on in terms of regulating legal conduct. But the students were living in student housing and are therefore subject to the rules of student housing. If Gonzaga was owned by the LDS and wanted to regulate the possession of caffeine in University owned or operated facilities, they would have a right to do so. Just as Gonzaga (and probably other schools) chooses to do with alcohol and firearms. Or for that matter the military for personnel residing in base housing.