The icon is for tab/list view. Maybe its an tiny bug with the detection for wider screen. You seem to trigger something at least, it seemsView attachment 327774
I can't tell what this is supposed to do.
It doesn't do much as far as I can tell.
It reduces the space between the forums in the forum listing but is that the intended effect ?
It doesn't expand / collapse the forums.
The exit out of the forum button (far right) is almost too accessible.
The bookmarks I add on the desktop, don't seem to make it over to the app.

For the exist button, alright, noted, but its a pretty common feature position. I will consider a better solution.
For bookmarks, these are different from the app / native feature only while the desktop is a plugin. So that is intended.