From the pics, it is 12.5mm at its widest. If this were 24mm, then we are looking at a crop factor of 1.92.
Working backwards, you will get the following sensor dimensions:
Diag: 22.5 mm
WxH: 18mm x 13.5mm
This means this sensor is halfway between the old 1.5" and the m43 sensor. i.e. It has about 8% smaller surface area than 1.5" and about 8% bigger area than the m43.
This matches the mpx count as well. The G1X sensor was 14.3mpx. The mark II is about 8% less at about 13.2mpx.
I think it's the same 18.7mm x 14mm sensor, just used as 18.7mm x 12.5mm in 3:2 mode and as a little narrower in 4:3 mode. So, you're always cropping a few sensor pixels.
You are probably right.