Whether the aim is to give the game an ambiguous ending or a poignant feeling, more detail was needed. It's so short and so minimal that it makes you wonder what the point was, not which of several explanations is the real one.
(Spoiler - click to show)I definitely assumed the viewpoint character was the spirit of the dead person given their reactions to the mourner, but the game never built up the kind of eerie atmosphere or sense of magical realism that would have been needed to make that obvious but not certain. Since the game maintains a fairly banal, literal tone, I wanted to see a more literal ending.