Barong is actually short for Barong Tagalog, which describes the formal men's wear of the Philippines. It is properly referred to as the 'Baro ng Tagalog' (dress of the Tagalog). Contracting the first two words produces 'Barong,' which literally means 'dress of.' So, if we want to be correct, we wouldn't say just 'Barong.' But, the slang way of referring to one of the beautiful formal shirts is simply Barong. Yes, the Barong Tagalog is a dress, a garment, a coat in itself. It is not merely a 'shirt'. If it were, then it would need a coat or a jacket over it to qualify as formal wear and would have to be worn tucked inside the trousers.
'Baro' = Word for 'dress' in the Philippines, Tagalog dialect
'Baro ng Tagalog' = 'dress of the Tagalog' describes the formal 'dress' or upper garment for men in the Philippines
'Barong Tagalog' = contracted form of the above
'Barong' = literally means 'dress of' - but commonly used to refer to the formal men's wear in the Philippines