I am bipolar and have been sober nearly 10 years now.
In my opinion the passage:
There is the manic-depressive type, who is, perhaps, the least understood by his friends, and about whom a whole chapter could be written.
simply means that a manic-depressive (bipolar) person can have difficulty maintaining sobriety if they do not also address their mental health issues.
I have worked hard over the years to get the bipolar stabilized. It has been a more difficult fight than getting sober. While drinking my bipolar did not matter as the alcohol seemed to help stabilize it. It became very pronounced once I quit drinking. That made it very hard to stay sober in early sobriety although I did stay sober because I had a strong support group and worked the Steps promptly so I could understand and apply them to my life.
I maintain my sobriety through AA but I also maintain my mental health by seeing a mental health provider and taking the medications necessary for me to treat my disease.