[kazinator]

As soon as two or more separate applications share some common body of code that helps them deal with The Computer, you have an operating system. It doesn't matter whether that common body is a table of software traps that dispatch machine language routines, or whether it is Smalltalk objects.

Some game on a MS-DOS floppy disk that boots itself from the boot sector and uses BIOS calls has an operating system.

The set of requirements which describe the host environment (the "virtual machine" in the classic sense) that forms the backdrop against with an application is developed is the operating system.

The only way you don't have an operating system is when the application itself does everything it needs with regard to the outside world by itself poking at I/O registers, and handling every interrupt and so on. Anything independently organized for that purpose, given something resembling an API, is an operating system.

There is, or used to be, a sensible version of "there should not be an operating system" I first heard some decades ago. Namely this: "there should not have be an operating system with a hardware-protected user/kernel boundary". The idea is that there doesn't have to be kernel which the hardware conceals using privilege levels and fences. The idea is supported by the notion that all security can be handled at the software level. The system, as such, is somehow verified to be correct. The only way to execute code is via compiling it via the system's trusted compiler, which generates only safe instruction sequences. Those sequences can call functions in the system, and those functions sandbox what can be done. All notion of trust and privilege is software-level without any privileged instructions having to fall down a trap into a privileged kernel which meticulously validates arguments.

(All that rhetoric needs to be somehow adjusted for 2021, which finds us jaded by knowledge of side channel attacks, cache attacks and whatnot.)