He is easy to miss as he is not on the surface and so you cannot see him from a distance. Rothman is in a hole, just around the corner from Yup'ik. Approaching the hole will trigger a cut-scene where Rothman pleads you to help him out of the trap.
Mindreading reveals Rothman is praying devoutly to the Divine, and promising to attend church if he ever makes it out alive.
In order to free him, you will need a rope, which you can find just inside the entrance to the inn, laying on the floor.
After freeing Rothman, there is a short cut scene of a troll arriving, which you must then kill. Be careful, the troll can kill Rothman which will cause you to fail this quest. Once it is dead, Rothman rewards you with his bow, explaining that he is giving up the life of a hunter and resuming guard duties.
Rothman will narrate parts of the story to a fellow guard if the Dragon Knight is within range.