This is saying that there is degenerative changes (arthritis) in the joints of the spine, as well as a small disc bulge which could be putting pressure on the spinal cord and the nerves on that side.
This could be potentially "pinching" the nerve, specifically C6, and causing pain to radiate down into your shoulder, upper and forearm, and into the hand, specifically the thumb and index fingers.
Ulnar neuropathy can explain finger numbness in the 4th and 5th digits of the hand, but I agree with you that it would not be responsible for shoulder and upper arm issues (typically).
So - based on the report, I would say there is a chance that your pains could still be attributed to your neck issues. I would want to get a second opinion from another spine surgeon about the MRI, and if they look at the images and feel that this could not be an issue, then considering looking at the shoulder may be helpful.
I would lean away from the shoulder, as people with rotator cuff injuries will tend to have worsened pain with overhead throwing motions.