If you think about an historical figure, such as Thomas Jefferson, although he is dead and buried (body has decayed) he lives on through his influence on history. We may even make a movie, trying to bring him into modern times, in a way that makes it easier to relate or associate, (revisionists; living and changing). The body died, but the fruits of his spirit (intellect, emotions, etc), continue to have an influence. These live on.
I think atheists speak from the heart. Maybe the athiest influence may not last very long. That influence may be more based on the short term impact of the living, which is the animal standard. The influence of the dead pet may linger among the immediate family, but it will fade away quickly from those less connected to the pet.
The spirit of Christ (intellect, emotions and intuitions) has lingered for 2000 years and will linger even longer. This influence or spirit is alive in that it still has an impact on bodies that still breath. Some of those, through this influence, become motivated to achieve perpetual life of through their influence on others; saints.