These displays are passive reflective LCD displays. The LED is only used for backlighting purposes.
You're right that there are issues with refraction and diffraction at play here, especially with the multiple air/glass interfaces in the stack up. I would imagine refraction being worse at larger viewing angles than from 0 degrees (straight on). Diffraction plays a part in reducing readability at wide viewing angles and even viewing straight on.
The displays that are used in our beloved G-Shocks are cheap reflective passive TN displays. I think the bigger issue with these displays is that with TN, the highest contrast is not at 0 degrees but at an angle that's off of center. If you look at an iso contrast chart, the area with the highest contrast is a blob something like 10-20 degrees off center in the 6 o'clock direction. That loss of contrast looking straight on might be perceived as loss of sharpness since the digits aren't as dark as at off angles. If I was a Casio engineer, I would design the display to have the highest contrast off center as most people would look at it off center, for quick glances.