What is gothic literature?
English Gothic literature began in 1765 with Horace Walpole's The Castle of Otranto, which contains all of the characteristics now thought to encompass the genre. A work does not have to contain all the following elements to be viewed as gothic, but it must have a healthy combination of them:
-horrifying events or the threat of such
-a castle, preferably haunted (in the case of "Mariner," feel free to substitute a boat)
-dungeons, catacombs, crypts, etc.
-labyrinths, dark corridors
-extreme weather and/or landscapes
-a hero whose hidden identity is not revealed until the end
-a heroine who needs rescued alot
-shadows/moonbeams/strange sources of light
A sub-genre known as Southern gothic also deserves to be mentioned, with many of the same characteristics transposed to Old South settings, but I assume by your reference to "Mariner" that you will be dealing with the English gothic.
Hope this helps!