How to call nested react function

You could use something along the lines of a revealing module pattern. Keep private variables in scope to gameCode and export the public vars and functions that you need.

const gameCode = (function () {
  const a = 1;
  function consolelog() {
    console.log(`success${a}`);
  }
  return {
    consolelog: consolelog
  }
});
export default gameCode;

In your other file:

import gameCode from './gameCode';
componentDidMount() {
  const gc = gameCode();
  gc.consolelog(); // success1
}

DEMO

Your Game class doesn't have a gameCode method so you can't use this.gameCode inside any of it's methods.

If you imported the gameCode inside the js file, you can use it anywhere inside:

componentDidMount(){
    gameCode();
};

The problem here is that the function gameCode in your example doesn't do anything - it only define a new function (locally) every time you call it. It's not an object that you can use to call it's function...

If gameCode was an object, you could have use:

gameCode.consolelog(something);

but it's not

You can change the gameCode to something like that:

export default gameCode = {
    consolelog: function (a){
        console.log("success!");
        console.log(a);
    }
}

And now since gameCode is an object, with the consolelog attribute as a function, you can use gameCode.consolelog(...) inside your Game class.

First of all, you don;t need to call it with the this key word once you imported it. You just call it that way: gameCode();.
Second, you are not returning anything from this function, hence you can't access it's nested function.
I think you need to re think the way you expose objects and functions.
For example, GameCode.js can look like this:

 const consolelog = function (a){
    console.log("success!");
    console.log(a);
 }
 export consolelog;

And then import it in your component:

import {consolelog} from '../utility/gamecode';

Edit
As a followup to your comment, if you need a function that will nest other functions and variables then you can create a class;

class GameCode {
  constructor(){
    this.consolelog = this.consolelog.bind(this);
  }
  consolelog(a){
      console.log("success!");
      console.log(a);
  }
}
export default GameCode;  

Then import it in you Component:

import GameCode from '../utility/gamecode'; // notice the import for default exports