If we didn't have a viewpoint/person to where these rays were directed, in what directions would these rays point while underwater?
I don't know if i understand your question. Wouldn't all the rays be pointing in the same direction regardless of if the person was there to view it?
The picture makes it seem as if the light is going towards the person's eyes. How does the water affect the direction of the light from the light's perspective as opposed to the person's perspective.
I think this phenomenon is a really cool application of Snell's Law, as the difference in the refractive index between air and water causes the light rays to refract in this way. Wikipedia has a picture of what can be seen from the underwater viewer's perspective: https://en.wikipedia.org/wiki/Snell%27s_window#/media/File:Snell's_window,_St._Louis_Zoo.jpg
This demonstration of Snell's Law is really striking. Here's a photo of Snell's Window from a pool in a city: https://www.flickr.com/photos/jtbss/9393445794