What is the cheers mate nans joke?

This insult suggests that the DJ or creator is overestimating their skills or importance. By comparing them to a “nan” or “grandmother” at the top of the stairs thinking she’s the formidable Chaser, it paints a picture of someone who is deluded or out of touch with their actual abilities or standing.
The word Chaser is related to the British game show The Chase, in which a seasoned quizzer plays the role of “the chaser,” attempting to catch competitors by providing more accurate answers than they do. The chaser is portrayed on the program as being aesthetically superior to the competitor, as though they are at the top of the steps/stairs when competing.