Hapkido in the modern form was created during the era of Japanese occupation of the Korean peninsula. It is a martial art created by combining the traditional striking arts of Korea with the japanese art of aiki-jujitsu. This means that it does in fact contain punching, kicking, knees, elbows, throws, reaps, ground fighting, etc. So in a nutshell, yes Hapkido is technically "MMA".
However unlike the modern MMA, hapkido teaches with full intent of self defense and the ability to maim. This means that there are techniques in Hapkido that will never be taught at an MMa gym, such as standing joint locks the most devastating throws, hooking into pressure points or striking pressure points, some techniques of Chinese decent, weapons such as canes or dan bongs. In order to learn Hapkido to it's fullest, a student cannot actually call themselves an MMA fighter.
-Notes: Most traditional martial arts contain all levels of fighting or some way to deal with other levels of fighting. What makes an "art" "mixed martial arts" is that the "art" is formed by multiple other arts and thus is a combination of many forms. The difference between mixed martial art and traditional arts is simply in the creation of the art.