Aside from all else, this will fail for lack of provable damages.
It's not even like Arthur had to rent a hotel room in lieu of expecting to sleep the night in the dorm room. That is not allowed, after all.
By the rules Arthur and Alice were aware of, Arthur already had to make alternate arrangements for where to stay after midnight.
And Arthur did have access to the dorm from 5pm-7pm, so the only time he could possibly claim damages for would be 7pm to midnight. Now, the walls close in on Arthur.
If Arthur had expected to store his traveling luggage there, the rule has not prevented it since Alice could simply fetch it for him at Midnight, since she is still allowed in. Arthur would need to show that is impossible.
Arthur already had a duty to obtain accommodations for the time period after midnight, when it's ordinarily expected that a person will need sleeping accommodations. It is essentially standard in the accomodation business, that a place which allow occupancy from midnight-8AM also allows occupancy 7pm-midnight. So Arthur could move his stuff there, or even move his social encounter there. To claim damages, Arthur would need to show that was impossible; and that the impossibility was reasonable (i.e. There was some reason he couldn't select a different hotel with sane/normal rules).
Even if Arthur planned to sleep rough or stay up all night, he would have to show how that was nowhere else to be from 7pm-midnight or that there was nowhere to spend those hours, such as department libraries (generally open to the public, often late hours), student union, off-campus pizza place, bar, city park, what have you).
Lacking these provable damages, the case will quickly be dismissed.
Further, if defense digs up other cases of poor merit, Arthur could be ruled a "vexatious litigant" and barred from further suits (except by approaching a judge for preapproval for a case; thus if someone crashes a plane into his house, he still has access to the legal system).