Is it possible to measure the working memory of a non-human animal? Is it possible to measure the working memory of a non-human animal? And if so, have there been any studies that have quantified the working memory of animals, and that have compared that to the working memory of humans? Or are the two not comparable?
Sure. For example, working memory can be assessed using the delayed match to sample task. Here are examples from monkeys, rats, pigeons, and bees.

The problem with comparing them is that the actual stimuli used for each species are different (e.g. odors for bees, shapes for monkeys) and this is known to affect the results. 

In humans, if you run similar tasks, just with small verses large sets of possible stimuli, for example digits verses general words, you can get very different results. Even if you did try to use the same stimuli set, the result will probably not be "subjectively" equal to that of a different species. Think of yourself trying to do the odor task of the bees; it's not a fair game.

Other seemingly small changes in the paradigm can also affect the results, for example a delay between the trials, etc. So the only way to seriously compare them would be to conduct the same experiment, by the same lab, of different species. I personally don't know of any research that was directly aimed at comparing them. Maybe someone using (lesioned) animals as a model for dementia would know more.