No, being an operator isn't about whether or not it's got two operands - that's the difference between a unary operator and a binary operator (and then there's the conditional operator with three operands, which is an example of a ternary operator). For example, + can also be a unary operator:
var x = +5;
You can sort of thing of operators as "built-in functions". They're known about by the JavaScript engine itself, and are part of the language rather than just being library features. (Although operators can often be overloaded by libraries, depending on the language. I don't know if JavaScript supports operator overloading, offhand.)
In some cases (JavaScript being an example) there's a bit of a blurring between the language and the standard library, but think about what typeof
takes as an operand: it's the name of a type. That's not something you can use normally as a function argument; it needs special support in the language.