Family Drama
The story starts out focusing on the tensions between Elizabeth and Walt (which ostensibly stem from his fondness for drinking and generally unseemly behavior), and you think those two are headed for a huge blowout when he finally gets home, Jerry Springer-style. Elizabeth even loses her cool in front of the kids and rails against his nasty behavior:
It is a scandalous thing as a man can't even come home to his dinner! If it's crozzled up to a cinder I don't see why I should care. Past his very door he goes to get to a public-house, and here I sit with his dinner waiting for him—. (1.59)
Yikes.
Of course, the story soon takes a total left turn, becoming less about when Walter will come home drunk and more about whether he'll come home at all. As you already know, of course, he turns up dead, and the story follows the family's reaction to his death.
For a short story, it packs in a lot of family drama, so we think it's a textbook example of this genre.