Many editors / IDEs (e.g. Notepad++) can directly connect to the FTP server, so working on a FTP servers looks almost same as working on a local folder. You just make changes to the files, and then refresh the web browser to see the changes.
Version control at least is essential for something of any size with any number of people working on it. You must be able to "revert" a set of changes quickly and reliably if the application has any importance at all.
Don't want to be rude here, but version control is clearly not "required" in the strict sense. Plenty of software has been developed without it. Now I wouldn't want to work at a place without version control either, but it is as required for developing software as seat belts are required for driving a car. Less even, since at least for seat belts they are required by law.