And my bet will be that they wanted to keep user's expectation of what he/she is sharing vs what actually is getting shared as close as possible.
A simple user believes he is sharing a screen resolution image and there's no hidden details in it.
>videos, which I'm sure they are using the actual camera
This is why when you start recording a video on Snapchat, there's a delay before the recording starts, and usually also a short delay before audio recording starts (especially noticeable if you have audio playing from your phone at the same time)
My bet is on that it's simply faster to take a screenshot of the viewfinder of the camera than using the camera to take a photo. Open up the camera already has some delay, taking photos introduces more delay before you get the actual bytes to do the processing. Taking a screenshot tends to be instant though, so in order to take photos the fastest, you can take a screenshot of the viewport.
Although this wouldn't work for videos, which I'm sure they are using the actual camera to do, instead of taking ~25/30 screenshots per second.