What classifies as a React functional component?

Any function which takes props as an argument can be classified as a functional component?

No, props is just the function argument, like all other normal function arguments. So if we define any function that accepts an argument it will not necessarily be a React functional component, like this is not a React component:

const Testing = props => {
   const a = 10;
   return a * props.a;
}

The important part is "If that component returns a React element", only then will it be a React functional component.

To make it more clear just define the below function in a separate file; it will not throw any error when you transpile:

const Test = props => props.key * 10;

But if you define this below component in a separate file without importing React, it will throw error, React is not defined, when you transpile:

const Test = props => <div>{props.key * 10}</div>;

Because JSX will get converted into React.createElement(....) and React will be required. The converted version of the above component will be:

var Test = function Test(props) {
  return React.createElement(
    "div",
    null,
    props.key * 10
  );
};

I will suggest, use Babel REPL and define both the functions and check the output.