I believe it is speaking of spiritual death, not physical death - the same with God's warning to Adam and Eve - hence they didn't physically die on the day they ate of the tree. When you think about it, this also makes sense of why animals physically die even though they didn't sin.
Giving dying arguments the breath of life by interpreting words on a spiritual plane is notoriously employed by fundamentalist Christians.
Lemme give you an example: "Christ returns in 1914 so the End of Days is due then", but nothing happened to the faithful in 1914! so "Christ's return was invisible aka spiritual; End of Days postponed until further notice".
Handy abracadabra, isn't it?
I'm not contending that this scripture necessarily means a clean-slate start after death/resurrection. I merely find it very puzzling why we can't let the Bible speak for itself? If it doesn't say death of the spirit and nothing in the context indicates it should, then there is no reason to make that assumption.
Also, if we DO go along with the spiritual death interpretation it still doesn't explain the reason animals die. It matters not if animal death is physical or spiritual. The question is why, not how. Why do animals die at all, even if they are dying in a spiritual sense, whatever that means?
INQ