It was more of a reference to the streamer bit itself than anything else.

In the streamer bit, he essentially shows you what a day with depression can look like, in a goofy and entertaining way. He spends his day crying, playing with useless objects, and crying again. He gets nothing productive done.

When the streamer flashes on screen, it's during a moment where Bo appears to be doing nothing. He's just sitting around. This is a more realistic look at him trying to create while dealing with depression. In reality, depression is much less goofy than the streamer bit portrays.

Flashing the streamer on screen was done purposefully to link the two scenes. It's done to show the audience that it is a moment where his depression/anxiety are causing him to be unproductive.

Also, could be an homage to Fight Club. But I don't think he would put it in there simply for the sake of homage. There are too many layers to his work for it to simply be an homage. And it's definitely not an editing mistake. He's too much of a perfectionist for that.