- an "extended machine": provide usable abstractions over the hardware to reduce complexity to a manageable level
- a "resource manager": provide for an orderly and controlled allocation of the processors, memories, and I/O devices among all the various programs wanting them.
By that definition, Linux is very much an operating system... unless by "Linux" you meant the kernel only without the additional tooling (systemd, libc, coreutils, shell, etc.) that distros ship with.
Many computer users run a modified version of the GNU system every day, without realizing it. Through a peculiar turn of events, the version of GNU which is widely used today is often called Linux, and many of its users are not aware that it is basically the GNU system, developed by the GNU Project.
There really is a Linux, and these people are using it, but it is just a part of the system they use. Linux is the kernel: the program in the system that allocates the machine's resources to the other programs that you run. The kernel is an essential part of an operating system, but useless by itself; it can only function in the context of a complete operating system. Linux is normally used in combination with the GNU operating system: the whole system is basically GNU with Linux added, or GNU/Linux. All the so-called Linux distributions are really distributions of GNU/Linux!
You wouldn't tell your mom about this great operating system she should use named "GNU/Linux". That's bad marketing.
Like, I'm glad for the solid kernel, but it's just not what I interface with on a daily basis. Same that I'm glad the car engine is running fine, but I care about the car, not the engine.