A "dry drunk" is someone who is an admitted alcoholic, does not go to meeting after having been exposed to AA, then goes on to live life without a drink and does NOT work the AA program.
In other words, they have quit drinking but have done nothing to change the person they were while drinking. It can be something obvious (anger, depression, etc) or something less obvious.
A "dry drunk" is not easy to quantify unless you have had a lot of experience with the person and know the person personally.