Can you please advise whether shipping companies who provide only logistics service come under the new VAT introduced in UAE?

As long as an orgnisation provides service with consideration (money or part money) it falls under VAT complaince. What is Exempted is Pessanger transport (Like Metro or Bus),  but there is a slight modification if  it is a Freezone company and services  between freezone, But services provided to mainland companies falls under VAT.