Not only are quote marks not necessary, I would find it odd to see them used. But I would also find it odd to see "... the United States of America (USA) ...," although i guess if it's a part of a big report where many other country names are used and abbreviations provided, it might do for consistency.
The question becomes a little more complicated with names, I think -- or maybe it does just for me. For abbreviations of countries, companies and the like, I would not use quote marks. But if I were using a name by which I wanted the reader to call someone -- or to recognize someone in a story -- then I might, e.g. Mrs. Beatrice Ruth Baxter ("Betsy").
I don't think I would bother with Mr. Mak Chui Feng ("Mr Mak") because I would expect people to call him Mr. Mak without having to be told. But if he had a nickname that he prefers to be called, then I probably would, e.g. Mr. Mak Chui Feng ("Jimmy") or ("Ah-Feng").
I agree with the second part of your response, and I would not even use brackets to define the abbreviated name; assuming there is only one Mr Mak mentioned it is obvious who I am referring to next time the individual crops up in the text.
Where do you live? I was wondering if you really are a native UK speaker?
The use of inverted commas and brackets looks a bit excessive to me, but maybe it's familiar in certain work contexts? Copyright seems happy with it, but he's an "American".
Quotation marks are often used in legal texts, either to indicate the short name of a party, such as the Acme Roller Skate Company ("Acme"), or a short identifier, such as for the bank that is lending the money ("the Lender"). In normal text they're not wanted.