I guess it is a music journalists' metaphor, once clever and then turned cliché. It describes a voice that sounds as whisk(e)y tastes: rough, smoky, yet enjoyable. The cause may or may not be drinking. Songs about a consumptive, yet somewhat stylish way of life, such as a whisk(e)y addiction, are deemed adequate for such a voice.

I have the feeling that whisky is considered more stylish (diseuses), whiskey more desparate (Waits etc.), but I may be wrong.