A "Character" in a play is an active participant in the drama, the conflict.  The main character, the "protagonist", goes through changes in character or worldview.  But mant other characters, sometimes called "Horatio" characters, serve various other functions--to help "visualize" the draaaaama, etc.  Here, the sea acts as the "antigonist"--the force fighting or in conflict with the protagonist (here, the mother).  Of course, the sea does not change ("No man can be living forever, and we must be satisfied.")  As for not appearing on stage, there are many occasions in drama when an important dramatic component is referred to only.  For example, General Gabler, Hedda's father, like the sea, a driving force.