I'd say because the clock wasn't his but was part of a furnished suite that belonged to whoever was GM and if Hanlon were fired it would just be one more perk in life he'd be going without.
Just watched an Italian horror film from 1972 " So Sweet, So Dead".
The police detective, Farley Granger, solves a murder by recognizing the chimes of a clock on a tape recording of a phone call the murderer makes to him!
Interesting...the reversal of the clue in "Most Crucial Game" and it came out the same year, 1972. I wonder if one inspired the other or if it was a case of great minds thinking alike?