The Bible teaches that death entered the world because of man's sin. So far so good ...
"Wherefore, as by one man sin entered into the world, and death by sin: and so death passed upon all men, for that all have sinned:" Romans 5:12 "Nevertheless death reigned from Adam to Moses," Romans 5:14 "For since by man came death, by man came also the resurrection of the dead." I Corinthians 15:21-22 "For as in Adam all die, even so in Christ shall all be made alive." Again, no quibbling over these scripture passages as presented, but how will the 'all' be applied by the one citing the passages? ...
Some Christians are committed to the idea that the earth is billions of years old. The biggest obstacle to this is the fact that there would be death before sin. And here's where conflating two very different concepts begins to breed confusion ... These teachers often say that there was death before sin since Adam would have eaten (and killed) plants. Killed? As in killed the cell level life and thus a soul level life, or is soul level life without a spirit the nature of plants and animals? Do plants have a soul? It is not clear because the author of the essay has conflated two completely different concepts: death of the soul --where there is a spirit component-- means God's life left the spirit and thus the soul suffers death, and Jesus addressed these two differing meanings of 'dead' on several occasions, most notably when He said 'Let the dead go bury the dead'.
The Bible passages cited are addressing death on a soul/spirit level not a cellular level. As the Genesis account shows us, life speaks from the Spirit to create not only the universe of inorganic but the organic also. But the organic have differing levels of 'life expression'. Where there is no soul (as with plants), the Spirit of God's creating power sustains the plants and perhaps bacterial level life.
The excerpted portion is from an essay which switches between death of soul and death of cellular life without differentiating and in fact conflating the two. Animals are souls, with bodies ... The Holy Spirit created the universe and embued life to cellular level things, but animals have a soul from which life flows, thus they are a different 'species' of life expression. Plants are bodies. Animals are souls WITH bodies. Humans are souls with a spirit component AND a body. Death entered the world for the animal kingdom AND for man ... Adam's spirit component had the 'godness spark' removed thus bringing 'death to the soul' because of a dead spirit. With Adam death to the soul entered the universe, and since animals have souls (but no spirit component), death entered the animal kingdom through Adam. By Christ, this 'curse' of death to the soul is ended and awaiting expression at His return.