The 50-year-old was originally taken to Caithness General Hospital and was transferred to Raigmore in Inverness, where he died on Tuesday.
During the brief private hearing at Inverness Sheriff Court, Rothwell made no plea or declaration and the case was continued for further examination.
He was remanded in custody.
Emergency services were called to Barrogill Street at about 9.30pm on Saturday following reports of a disturbance.
A police cordon remains outside as officers continue to investigate the incident.
Detective Inspector Craig Still warned residents to expect activity in the area for some time to come as inquiries continue.
He said: “A police presence will remain in the area whilst inquiries continue and I would like to thank residents for their patience during this time.”
Police are appealing for anyone with information to come forward by calling 101 or Crimestoppers on 0800 555 1111.
