This question is another way of asking, "Does this poem qualify as a ballad?" The answer is "yes," but let's examine each of the three qualifications contained in this definition of a ballad.
Does the poem recount a single episode? In a sense, the poem functions as a "story within a story" or a frame story because it relates one story about the mariner pulling aside a wedding guest, which happens in the present time, and another story about what happened to the mariner at sea, told in flashback. However, the stories are not two separate tales; indeed, the present time story is an outgrowth of the prior story and is really just a continuation of it. Because of the mariner's experience at sea, he is now compelled to roam the earth retelling his tale to people who need to hear it. So although part of the story is told in flashback, the poem has no subplots or secondary plots; it relates a single episode.
Second, is it dramatic? This word has two definitions, and both apply. One refers to the art of drama, where there are actors in a play who enact a series of events. This definition applies in the sense that the poem is a story with rising action, climax, and denouement and features memorable characters. The second definition for "dramatic" is "striking." The events in the poem are certainly striking. The poem features spirits, battles with nature, life-threatening situations, and even "zombies."
Third, are the events "often tragic?" This can also be answered affirmatively. Some of the tragedies that occur in the poem are that 200 sailors die, two spirits--Death and Life-in-Death--gamble for the life of the mariner, a young boy goes insane, and the mariner himself does rigorous penance for causing what the poem presents as a grave tragedy itself: the killing of the innocent albatross.
This poem easily conforms to the definition of a ballad by presenting a single dramatic and tragic story.