From the poem itself it is almost impossible to confirm what the father does for a living. But one can guess that he does something related to books from the line “his bag stuffed with books is falling apart”. So it may be selling books, publishing, or even teaching. 
 
But the poem is rather autobiographical. The poet’s father Purushottam Chitre was a literary enthusiast and used to publish a highly regarded periodical Abhiruchi.