The War could potentially exist with cool down periods- say the Western Front Stalemate is never broken, and becomes the statues quo, with France and Germany repopulating behind the scenes. Russia collapses, with Germany asserting dominance there, whilst America sells both Entente and Central Powers weapons. The Ottoman's collapse into a bloody Civil War, with each major ethnicity battling one another.
There is still a lot of areas in the world for conflict to erupt; Africa and the Americas spring to mind.
There was fighting in Africa...