But that's the thing, it's only managing processes, not scheduling them nor managing the minutia of their stacks — it devolves that responsibility to the real kernel by using 'dumb' native processes instead of inventing its own fucked coroutines with a browser-wide GIL for all the logically-independent javascript environments.
Correct, it is not an operating system. Just as the Java Virtual Machine is not an operating system. But when you start using principles and common designs from operating systems, you are approaching the design of an operating system.
It is less OS-like than any other major browser!