Author of the book 'Shatranj Ke Khilari' is

Books-and-authors questions in general awareness test recall of a literary work's actual creator, verified against publication records and biographical references -- and, when a work has been adapted into film or other media, the adaptation's own credited source material confirms rather than changes the original author.

Applying this to the story named in the question:

• 'Shatranj Ke Khilari' (शतरंज के खिलाड़ी, "The Chess Players") is a Hindi short story by Premchand, first published in the Hindi magazine Madhuri in 1924 and later included in the story collection Mansarovar.

• Its author is Munshi Premchand (Dhanpat Rai Srivastava, 1880-1936), one of the most prominent Hindi-Urdu writers of the early 20th century.

• The story is set in Lucknow during the reign of Nawab Wajid Ali Shah and follows two noblemen so absorbed in a game of chess that they remain oblivious to the British annexation of Awadh unfolding around them.

• The story's wider recognition also comes from Satyajit Ray's 1977 film of the same name, which is explicitly credited as an adaptation of Premchand's story -- confirming, rather than altering, the original authorship.

Cross-checking against the other names listed: Mahadevi Verma's documented body of work belongs to the Chhayavaad poetry movement (Yama, Neerja, and related collections); Kiran Desai is a contemporary English-language novelist (The Inheritance of Loss, Hullabaloo in the Guava Orchard); and no literary author by the name Beena Seth is documented in standard publisher or literary-biography reference records. None of these is linked to 'Shatranj Ke Khilari'.

Hence, the author of 'Shatranj Ke Khilari' is Premchand.