There are two parts to answer that question correctly. The TERM "dueling pianos" came from the 1890's when ragtime players of the era would challenge each other in a DUEL on stage to see who had the fastest twenty fingers or earn the most tips.
The CONCEPT of Dueling Pianos originated in the 1950's at Pat O'Briens in New Orleans. There were three ladies named Mercedes, Connie Kay, and Sara Belle "Sue" Wheeler who trailblazed the concept and were the pioneers of modern day Dueling Pianos. In 1986 Alley Cats (in the Dallas Alley of Texas) would round out what we see in Dueling Pianos today with college fight songs, band sets, and roasts.