Sublime lets you have an arbitrary number of windows open, and closing one doesn’t quit Sublime unless it’s the last window; so if there are two windows open and you close one, you’re not quitting Sublime, you’re just closing a window
The hot_exit setting (which is enabled by default) tells Sublime that when you quit it, it should save it’s state into a session file and restore it on startup. The state saved is a list of all of the currently open windows, the files open in them, etc.
Windows can have a project associated with them; if that is the case then when you close the window, the state of that window is stored in a special workspace file that is associated with its project; opening the project recreates the window as it existed when it was closed.
According to what you said here, you had a window open that you were working in, then you opened the preferences window, and (presumably) go back to the original window you were working in. When you close the working window, you think you’re closing Sublime, but you’re not; you’re just closing the window.
That shows you the preferences window hanging around in the background, so you close that one too. Now you’re closing the last window, so the state of the application is saved: a single window that used to be the preferences window.
When you restart Sublime, the state of the application is restored; you get back the settings window that you had open when Sublime quit. The other window is gone now because you closed it. Your remaining window has your user preferences on the right hand side, but the left hand side of the window is now empty due to the way the default preferences were loaded into it.
According to your screenshot it looks like you opened up the folder you had open previously in what used to be the settings window. You can use View > Layout > Single from the menu to put the window back into a single pane if you don’t like the split.
However, the list of files you had open is now gone unless you happened to be using a project in that window (in which case opening the project will bring the window back the way that it was previously).
After a little more thought it occurs to me… It would be great if, upon opening settings, that window state were never saved. After all, the user is only concerned with the state of the workspace s/he is doing work in. It is understood that the settings view will be the same each time it is pulled from the menu.