This is called pixel vignetting. From a research article available freely here, the detailed explanation is that the actual light sensitive element is sitting at the bottom of a well and light can only fully reach the sensor (pixel) if it is coming straight on, right down the well.

In all cameras lens design affects lens vignetting. The lens has an 'image circle' which is designed to match the size of the film/sensor (which is why on FX cameras DX lenses vignette a lot). For digital cameras there is an additional source of vignetting called pixel vignetting.

In short, the individual pixels of the sensor physically sit at the bottom of an opaque well (the well is made of structural components and sensor electronics). This well acts as a collimator and reduces the intensity of any light that comes at an angle to the sensor. At the middle of the sensor the light is coming in parallel to the well and strikes the pixel full-on, generating the largest signal. At the edges of the sensor the light strikes at an angle and is largely cutoff by the well, resulting in lower sensor signal.

Camera manufacturers calibrate the vignetting of the sensor and correct for this in software. A detailed explanation is available in this research article. Some vignetting is also countered by having microlenses at the top of the wells to focus the light down the well.