TL;DR a droplet intersects the stream, temporarily diverting it.
The glass is not uniform due to surface contaminates like oil and dirt. This makes the binding energy between the water and the glass vary by location. A droplet that land on the glass with one edge on a high binding energy location and the opposite edge on the low binding energy location will move away from the low energy towards the higher energy.
Lets assume there is a uniform distribution of very small droplets hitting the vertical glass pane. At first all of the droplets will just move to maximize their binding energy and sliding down the glass would require losing more of the binding energy than they would gain from gravity. Thus all the droplets stick to the window.
As droplets continue to fall some land overlapping with droplets that were already there. These droplets reform to accommodate their new volume and mass. They might even slip down a little to bigger binding energy ledge. Their new binding energy loss/gain by sliding should be proportional to the diameter as it's only the perimeter of the droplet that changes. However, the energy gain from gravity is proportional to the diameter cubed. This means that as the droplets get bigger gravity will dominate and pull the droplet down the glass.
If you look near the top of a pane of glass where no water is pouring down this is pretty much all you see, droplets getting larger and larger until they slide off down the pane. If there are especially high and low binding energy regions you'll even see that the droplets tend to grow in the same locations.
However, for long panes of glass these sliding droplets will collide with other droplets, getting even bigger. Whenever these sliding droplets hit a droplet that is slightly to the side, it will be pulled towards that droplet slightly diverting its path. Additionally the surface binding energies will still pull the droplet so that it tends to follow a high binding energy path.
Eventually the droplet becomes so big and is moving so fast that it starts growing a tail where the water still wants to stick to the glass and the reduced surface tension of the large curvature isn't enough to rip it off. Another droplet coming along that happens to hit the tail will immediately divert to it as the already wetted surface acts like an extremely high binding energy region. This process is what accumulates droplets into streams.
These streams tend to go straight down, buy divert slightly to take advantage of higher binding energy regions. The cause of the sudden side track of a stream is a temporary high binding energy region in the form of a droplet. While all of the streams are making their way down the glass, the regions in between the streams are still accumulating ever growing droplets. When one of these droplets grows to the point it runs into a stream, the stream is diverted.
In the video it looks like the droplets landing on the window may not all be tiny, and thus this process is accelerated by big droplets appearing randomly, but the same effects can be observed (perhaps more clearly) by spraying a fine mist on a piece of glass.
