To me it seems almost the lineal successor to Dracula (1897) and the predecessor to Dr No (1958).
In all of these, the protagonist is battling an enemy that enjoys taunting and playing with his prey. The enemy lives in relative seclusion, but has plans to make a wider impression on the world and there is a battle of wits involved.
The enemy also has a mysterious background that crosses many eras. Count Dracula being centuries old, General Zaroff being a hangover from Tsarist Russia and Dr No a survivor of the early twentieth century Tong Wars.
Dracula is probably the outlier in being inherently supernatural, whereas in The Most Dangerous Game and Dr No, the enemy attempts to test the limits of humanity (Zaroff literally hunting the protagonist and Dr No forcing them to run a relentless obstacle course).
What differs in The Most Dangerous Game is that the protagonist ultimately sets himself up to become the antagonist, having acquired a taste for blood in the process of defeating Zaroff.
by LewisKOTyson
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If I had to identify a single antecedent, it would be John Buchan’s The Thirty-Nine Steps (1915). Both stories feature men being pursued by sinister forces across rugged landscapes and having to use their wits to escape. This same tradition led to Geoffrey Household’s Rogue Male (1939), which in turn influenced 1972’s First Blood (Rambo!).