I saw your thread and was worried that it was Murray who had been diagnosed with diabetes - glad it's not him.
Anyway, coming from a long line of diabetics (which I'm not, fortunately)... yes, molasses is a form of sugar.
With diabetes, you need to monitor simple sugars as well as complex carbohydrates which convert to sugar in your body. This especially means things made with flour (particularly white flour) which includes a majority of dry commercial treats.
If the diabetes isn't bad, then an occasional flour-based treat should be okay. The problem arises when the diabetes is being carefully controlled by medication - eating simple sugars (sugar, honey, molasses, fructose/glucose, etc.) will spike the blood sugar in a bad way. Complex carbs will also raise blood sugar levels, but not as drastically. In fact, a bowl of oatmeal (complex carbs) can be used to bring up low blood sugar in a gradual way. My diabetic grandma used to have oatmeal or toast every morning for just this reason - after a night of no food, she was very lethargic in the mornings and the oatmeal or toast would bring up her sugar level in a controlled fashion.
I guess I'm just trying to say that there can be hidden dangers to feeding diabetic dogs. I'd suggest making some high-protein low-carb treats at home - take a look in the recipes forum for treats that are meat based with minimal flours or grains.
Give Murray a hug from me and tell him Buster sends him a lick and nubby wiggle...