There are many products and things that control the global economy. The oil corporations are certainly one of them. There are many families over time who have controlled the world due to the products that they have created over decades and possibly centuries. Not all of them are involved in oil. Others are involved in stores, real estate, shipbuilding and other types of products.
The oil corporations definitely control the global economy to an extent. However, there are other things that impact the global economy. Politics and terrorism has some control over the global economy as well as products that are sold. Real estate that is unrelated to oil, also contributes to the global economy. Gold and other precious metals like diamonds control the global economy.