Both Ricoh G900 and Sony RX100 III have 20.0 MP resolution sensors but Ricoh G900's sensor is 1/2.3" (6.17 x 4.55 mm ) and Sony RX100 III's sensor is 1″ (13.2 x 8.8 mm ).
Since Sony RX100 III's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Ricoh G900.
Below you can see the G900 and RX100 III sensor size comparison.
As seen above, Sony RX100 III has a 4.1x Larger sensor area than Ricoh G900. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.