Well, adding "pure" or "straight" emphasises that the coffee is black. The question is, would this sentence still work in Russian without "чистый"? It depends if this is also simply an emphasis word, or if it is necessary to say "black coffee" in Russian.
EDIT: I just noticed that Kundoo already covered this in another comment. The word “straight”/“pure” IS necessary here.
Thank you for the reply. It was more of a cultural question. Apart from what the words mean, I was wondering if it was the normal way to say it - in English one typically would not say 'pure black coffee', as 'black coffee' itself means 'without cream or sugar'. Perhaps in Russia 'black' denotes a kind of coffee not what is or is not added to it?
Not really, I haven't heard someone say this, just black coffee. But we have an expression пустой чай, that literally means 'empty tea' as in tea without anything, mainly sweets, cookies, jam, etc., that usually goes with tea, just tea. but you can't say that to refer to a cup of tea without milk or sugar, it's best to specify if you want something in your tea, otherwise it'll be just simple black (green, white, red, whatever) tea.
You can't just leave out words because you don't like them. In Russian "чёрный кофе" means exactly the same as "black coffee" and adding "чистый" is also kind of redundant. But since the author felt the need to strees it, then it has to be translated or you are changing what they were trying to say.
To be honest, I can't say I've ever heard anyone say that, and I'm native. The phrase "Чёрный кофе" already means without milk or cream and (usually understood) without sugar. You can add "без сахара" to emphasize that part. The adjective чистый is usually used with alcoholic beverages though, and in those cases it would mean "neat".