Optical1: you have accidentally multiplied sensor diagonals with their widths instead of multiplying their widths with their heights, so your area numbers are wrong.
Correct numbers for 4:3 aspect ratio sensors are (source: http://www.dpreview.com/glossary/camera-system/sensor-sizes ):
1″ sensor: W=12.8mm, H=9.6mm, A=123mm²
2/3″ sensor: W=8.8mm, H=6.6mm, A=58mm²
1/1.7″ sensor: W=7.6mm, H=5.7mm, A=43mm²
Because your numbers, though absolutely incorrect, still were in correct proportions, your end results still apply: RX100’s 1″ sensor is little over twice the area of the XQ1’s 2/3″ sensor, which again is some 35% larger than the S120 1/1.7″ sensor.
As a comparison, a Full Frame sensor is 36mm*24mm = 864mm².
Started out doing photography at the age of 6 using an uncle's old 1940 kodak brownie box camera. At 15 years of age, I decided to buy my very own 1975 Praktica SLR camera. I now shoot with a Nikon D850. I do unpaid TFP and commercial paid work.