Do I need to import a node.js module to write to a file or is there some way to do it in-engine?

basically to save game in html5 way is use localstorage
but if you need more(read/wring file), yeah you have to include node module using electron.

The simpliest way to save data is using localstorage, as @reopucino said.

I use this class definition for saving using it.

- For game data, I use a game instance where I manage all the game elements and game workflow (for this example you can use your own approach). In this implementation, I don't use the game data. Feel free of implementing game  attribute as you want.  

- This is a generic class with basic operations, so you can extend it for a more specific data management (scores, saved games., archievements...).

- If you want to use another system for managing data (a database, a file...) you could override these methods.

For example, if I want to store data using a web API, I could use the "fetch" library or an XMLHttpRequest instance for sending data in the implementation.

The main advantage of using a solution like this is the abstraction for managing saving and load data that is provided to other modules: They don't need to know how or where the data is saved or from where is loaded.  

export default class Storage {
  constructor(game) {
    this.game = game;
  }
  load(key) {
    return localStorage.getItem(key);
  }
  save(key, value) {
    return localStorage.setItem(key, value);
  }
  add(key, item, value) {
    const entry = this.load(key);
    entry[item] = value;
    this.save(key, entry);
  }
}

And remember: games created with pixelbox are, in fact, html5 applications, so you can use any code that you can use for a web client application.