This is a new capability of the `choose-tree` feature in tmux 2.8. From [tmux(1)](http://man.openbsd.org/OpenBSD-current/man1/tmux.1#choose-tree):

> Key 	Function
> Enter	Choose selected item
> Up 	Select previous item
> Down	Select next item
> x 	Kill selected item

So after you've navigated to the right window, press `x`, then when you are prompted:

`Kill window 1?`

...press `y` to accept. This also works for killing individual panes, or even whole sessions.