It is up to the local bishop to determine what is an appropriate place for Mass. In general, Masses should be said in a Catholic Church or other sacred space (shrine, chapel, oratory, etc). If the Masses happen on a regular basis, the bishop must approve it, or he can delegate this decision to the priests. Most bishops give all priests the faculty to celebrate Mass in any dignified place.
When it comes to college campuses, the bishop has either appointed a chaplain for the campus, or it is part of the territory of the local pastor (often that will be the same priest anyway). While it isn’t possible for posters here to give a definite answer as to whether or not the local bishop allows this, it’s extremely unlikely given the fact that this is happening weekly, that it’s happening without the bishop’s permission, one way or another.
In other words, the canonical legality of the Mass is probably not something to be concerned about, unless there’s something very unusual happening–like a rogue priest saying Mass on campus to stay “under the radar” or some other unlikely scenario.
Most likely, the priest is celebrating Mass there for the good of the students on campus, and one way or another, has permission to do this.