This sounds like an unmanaged VPS service. While I would expect FTP to be already installed on such a VPS, it's not absolutely necessary to be so. You certainly have root access via SSH, which means you/your client could install an FTP server at any time, if you have the necessary skills.
The CEO told me that because it is a VPS that runs with SSH (no FTP access), I must have either the cPanel/WHM, which comes at a monthly fee, or I have to use a Linux-based operating shell (can't do that, as I don't run a Linux box). Does this sound right, guys?