Do I understand correctly that the structure is changed a bit? I see the other folder where settings.php is sitting now. So, should I copy this folder to the server too and move my actual setting.php into the other folder?
No.. the other way around
Actually, I think the settings.php is in the "Other" folder because it is not necessarily needed in case you are simply updating an existing 2.1 installation. Your existing settings.php should be enough, and doesn't need to be overwritten with a blank default file. Of course, there may be changes to that file too, so checking the changes isn't a bad idea.
The "other" folder contains all of the install AND upgrade files... when we build the actual release, we build two different constructs -- but the github version has both sets ina sub folder- expecting the admin to know which ones they need.