The very fact that we as humans are having this question demonstrates that we bring something to this earth that no other species do.
Humans bring an advanced level of reason and understanding of the world that no other species do. We are able to question the merits of our existence in a critical way. If humans were to die off, there would be no more art, no more literature, no more music, or painting. There would be no more science dedicated understanding the marvels of the universe.  We represent something of an awakening moment for the universe. For that reason alone, the extinction of the human race on planet earth would be a tragedy.
This presumes a significant knowledge gap between humans and other animals. It supposes that we are in fact the only species on the planet that engages in reasoned thought and the only species on the planet that creates art and carries out scientific experiments. Elephants and whales routinely display empathy. Vogelkop bowerbirds create art displays to woo females, with precise sculptures build not for their structural merits, but their artistic ones. Many species possess number-like skills and the basis for which humans developed mathematical understanding. We are not as unique as many believe. Therefore, we do not offer something no other species does, and it would not be a tragedy if we died out.
P1: Humans are the only species that engage in deep reasoning and understanding. P2: If humans died this would be lost. P3: This would be a tragedy.
Rejecting the premises
P1: Humans are not the only species that have these capabilities.