The 1-Inch Sensor Is Not One Inch, and the Name Is a 70-Year-Old Fossil
Check the active imaging area specified for the sensor inside a Sony RX100 and you get 13.2 x 8.8 mm, with a diagonal of about 15.86 mm. That is close to 16 mm, not the 25.4 mm that an inch is supposed to be. The "1 inch" printed on the spec sheet does not describe any dimension of the imaging area, and the reason runs all the way back to a glass vacuum tube that stopped being manufactured decades ago.