However, I think it would be significantly harder for us to wipe out all life on the planet earth. I'm hard pressed to think of anything besides blowing up the planet, or grey goo (and arguably grey goo would just be another form of life).
This war will be fundamentally a pursuit of energy and resources, as it has always been. And this pursuit of energy and resources has always been detrimental at an exponentially increasing scale to other life forms which depend on the same.
As an example, if there is a nuclear war in the Indian subcontinent, the countries there will only be acting out of their need to guarantee their survival. However, the resulting fallout will have extinguished life forms at a pace that doesnt have any bearing in history.