Caliphal decrees prohibited the playing of chess (the pieces of which are customarily figural) for iconoclastic reasons as early as the eighth century. It is likely that chess pieces of the abstract type, such as those exhibited here, replaced the figural ones in order to circumvent those decrees.
[ Saeed Motamed, Frankfurt, until 1975; sold to MMA]
Carboni, Stefano. "Chessmen in the Department of Islamic Art at The Metropolitan Museum of Art." Scacchi e Scienze Applicate suppl. no. 7, fasc. 15 (1996). ill. p. 5 (b/w).