This writer's short article, a delusion (4)
I believe the answer is:
myth
'a delusion' is the definition.
(I've seen this before)
'this writer's short article' is the wordplay.
'this writer' becomes 'my' (I've seen this in other clues).
'short' means to remove the last letter.
'article' becomes 'the' (the definite article in English).
'the' with its last letter taken away is 'th'.
'my'+'th'='MYTH'
(Other definitions for myth that I've seen before include "lie!" , "false interpretation?" , "(Urban?) story" , "A US president; a UK PM" , "Wildly-held but false belief or idea" .)