"To keep track of time along light paths, I will be using a slightly modified geometric optics model, in which light travels along straight lines at constant speed."

This is computer-rendering light, not real light.

A careful watching of the first video can incidentally reveal why we don't simulate real light. Watch as the first clean pulse of light spreads out and goes from this really-easily-characterizable expanding circle to an ever-more-complicated set of waves as it moves out into the world. You can't afford to simulate things as waves, at least, not with conventional computers.

Without trying to think too much over it (still haven't had my morning coffee), I think your representation of light corresponds to a wave vision. However, per wave-particle duality, you can also consider light as moving photons (particle vision of light) and then yes, every single photon moves in a straight light (tries to). So it depends in how you're trying to see light.

This is probably a really shitty and probably mostly incorrect analogy, but it sounds like you're describing Huygen's principle, which roughly says every point light travels can be thought of as a very weak point source. For example, loads of old buildings have hallways with an open window, and rooms adjacent to the hall way would have "light-borrowing" windows. So light traversing down the hallway could still emit light in to the perpendicularly facing windows.

There's some other stuff regarding light's wave/particle duality, so I don't know if there's a simple solution to whether it propagates in all of these paths, or as a particle moving in a straight line.