Since the limitation appears to be with regard to specific positions of the aperture diaphragm it is most likely a mechanical limitation of the camera's design. The limitations you have described are clearly outlined on page 49 of the Canon PowerShot G7 Advanced Camera User Guide, so this is expected normal behavior for this camera. As the focal length increases the effective aperture will change for the same position of the diaphragm mechanism so it appears the specific shutter speed limitations apply to a specific position of the diaphragm.

This would lead one to assume, without any confirmation available from Canon that we could find on this point, that the camera has a leaf shutter. The wider the selected aperture is (lower the f-number) then the amount of time it takes the mechanical parts to move from being closed to open all the way becomes more critical to the amount of exposure on the edges of the frame and depth of field of the entire frame, thus the longer/slower the fastest possible shutter speed is for that selected aperture value.

Don't forget that aperture numbers are the denominator of a fraction. At f/2.8 the effective aperture is 1/2.8th the focal length of the lens. At f/8 the effective aperture is 1/8th the focal length of the lens. The aperture settings that limit the shortest shutter speed to 1/1600 second are the widest settings (f/2.8 at wide angle), those that limit the shutter speed to 1/2000 second are the mid-range apertures(f/3.2-3.5 at wide angle), and those that allow a fastest shutter speed of 1/2500 second are the smallest apertures (f/4 and up at wide angle). All shutter speeds below the shortest value for a given aperture are also available with that aperture.