To deal with the many comments and points brought up, I have edited the answer yet again.
Is the BIOS an Operating System?
Well, if an operating system is defined as software that allows a user to interact with the hardware of a “computer” then yes… technically and literally it is an Operating System.
Does Task Switching define what makes an Operating System?
Considering that MS-DOS was a valid Operating System, and up until version 5 Task Switching was not supported, task switching does not affect whether or software is an Operating System.
Does Virtualization of Memory define what makes an Operating System?
Again, using MS-DOS as an example, although support could be added for memory virtualization by running extenders during the loading process, it was not necessary to use them. Thus, memory virtualization also is not a prerequesite to what makes up an Operating System.
If it is stored in Firmware, is it an OS?
Some would argue that a router doesn’t use an Operating System. For example, there appears to be contention as to whether DD-WRT is considered an Operating System. Are there devices that store an Operating System in Firmware? Modern phones, iPods, and more store complex operating systems that can have programs added to them in Firmware. So, just because an OS is loaded into Firmware, this does not exclude the software in question from being considered an Operating System.
If you can’t add programs, it’s not an Operating System.
Step away from a modern smartphone. Look at a cheap disposable cell phone. It has an Operating System stored in Firmware, but you cannot add programs. It runs as it is, and only with the functionality that is offered. You navigate through the menus as you would any other OS, you choose what you want to do (play games, etc) and with a good number of them from a few years back, they did not have the ability to add any additional software.
If it is not modern, is it not an Operating System?
The point in history at which the OS was created and launched has no bearing on whether or not it is an Operating System.
So, the BIOS may not be pretty, and it may not offer you extreme functionality. However, it is still an Operating System.