What made the Great War a worldwide phenomenon and is it correct to refer to this a world war thought most of the fighting took place in Europe?

Well most of the major fighting was indeed in Europe, but it wasn't exclusively there. There was also a lot of fighting in Africa and the Middle East, and there was even fighting in the Pacific- mainly Japanese, Australian and New Zealand troops occupying German colonies there.

In the Middle East, the British famously allied with Arab tribes and caused a revolt against the Ottoman Empire, which ruled the area. You may have heard of Lawrence of Arabia- he was the British officer who was instrumental in this.

Additionally, since the British and French had large colonies (with large armies defending them) in Africa, and Germany had smaller ones, a German general named Paul von Lettow-Vorbeck started a brilliant guerrilla campaign aimed at preventing the Allies from sending their African armies to help in Europe. For four years Allied armies chased his tiny army without success, and he only surrendered after the war had officially ended- he had never lost a battle.

So the war did happen all over the world, hence, world war. It can be argued that other wars were also "world wars". The Seven Years War is a good example of such- it was fought mainly in Europe, but also in Africa, North America, the Caribbean and India.