Nothing is literally dead in "The World is too Much with Us," but the speaker suggests that humanity's alienation from nature is a kind of double death; because people are obsessed with "getting and spending" they aren't moved by nature, and that makes them dead. And nature, since people no longer acknowledge it, is also sort of "dead." All this death makes the speaker wish he could bring an old religion back to life.
"The World is too Much with Us" is obsessed with death; humanity is emotionally dead, a condition signaled by the fact that their alienation from nature is characterized as the forfeiting of their hearts.
The people the speaker describes are partly dead, but they are also biologically alive; in a sense, they occupy a strange space between life and death. They are suffering a living death.