Thanks, everyone! This seemed like a nice "shortcut" but I guess we'll be looking elsewhere

Or, maybe you could use all those negative points mentioned by others to negotiate down the price of the setup. There is little chance that he will be taking the chicken coop and run with him when they move. At that point, it has no value to him at all. I know some people around here that are willing to give a coop away because they fear the new owners might not want to have chickens and it would be an expense for them to tear it down and remove.
I think the coop would be fine for 6 chickens, but not 12, and certainly not 18 like he said he had. The low egg production may be due to over crowding, poor nutrition, or God forbid "Egg Eaters!" Chances are that if they thought 18 chickens were OK for a small coop like that, they probably did not know much about raising chickens when they started.
I would not assume the chickens were only 1 year old. They should be laying a lot more eggs than what he says.
Yes, some people think they can only feed cracked corn to the chickens to save money and still get eggs. Our great grandparents used to do that on the farm. But you suffer in terms of egg production. Some people do not want to even feed kitchen scraps to their birds. I do, but it's not their main feed. In the summer time, my chickens eat lots of grass and I will see their commercial feed consumption go down by half, but their egg production also goes down. I have commercial layer feed available 24/7, but my chickens prefer to eat just about anything else before they eat the commercial feed. It sounds like your neighbor was not feeding his birds well, so I would not be overly anxious to inherit those birds.
Anyway, it is a nice small coop and run for a small flock. I might offer a low ball amount to see if he is interested in the offer, but be willing to walk away from the deal if the price is not right. I agree that the chickens themselves might be a problem given their past history and currently low egg production rates. Red flags there. I would go so far as to say the chickens themselves might have a negative value to the package. So, if you decide to go after this package, assume you might have to replace that flock with your own 6 hens if his flock does not respond to better care.
Bottom line, I think you are in a better negotiating position then your neighbor and if you can't come to agreement then walk away and plan your own setup. There is some satisfaction starting out everything from scratch, but, having done that, I would also consider the value of buying something already made and upgrading it to your needs.
There have been a lot of negative comments and warnings about this potential deal, and I don't disagree with those comments. However, it might still be an option if the price is right. I think the coop and run have some long term value, but the suspect health of the flock would concern me. The flock can be replaced and you could start over with your own chicks at any time. Some of us only plan to keep a flock for a 2-3 years and then replace them. So the birds are just a short term investment.
FWIW, my chickens stay in their coop most of the winter, and never go outside in the snow. I built my coop to have almost 8 square feet per bird, which is twice the recommended 4 square feet per bird normally recommended because I expected this. If you get 12 birds in that small coop for 2 square feet per bird, I still think you need to either reduce the number of birds or expand that coop. It just looks too small to me for that many birds. I think they need more room.