Local Controller reported witnessing an aircraft going off the runway during the rollout and saw it go into the grass. The pilot did not need assistance and proceeded to exit normally on the taxiway.

Narrative

I cleared Aircraft X to land on Runway XX and gave him a wind check. The aircraft was an APPREQ (Approval Request) by ZZZ Approach for Runway XX even though Runway XXL was in use. I gave the aircraft an additional wind check with the landing clearance due to him going to a runway that wasn't most closely aligned with the wind. Pilot was rolling out normally and suddenly darted 90 degrees left and left the paved surface of Runway XX completely. The aircraft ground looped in the grass; I asked if the pilot needed assistance and he said; No we will go back to [Taxiway] 1." He exited normally at [Taxiway] 1 and the Ground Controller coordinated a runway sweep. Deny the APPREQ. Pilot called the supervisor and stated he had no idea what happened. He said maybe it was a braking issue. That looked like what I saw; I believe the left brake was locked. At the time of this incident I had no real break from my last session which involved a runway incursion by a student pilot. I listed fatigue as a factor. EVERYONE in our facility is on 6-day work weeks. Often with 10-hour days. We no longer have sufficient staffing to ensure safety. As an example; I worked a XA:50 shift 3 days ago; followed by an XP:10; an XF:00; 9-hour shift; and an XC:00 today. This is a huge issue. Our circadian rhythm is destroyed here; a day followed by night; long middle; day."