index.js

class Snake {
  constructor(position, direction) {
    this.parts = [position];
    this.direction = direction;
    this.newDirection = null;
  }

  update() {
    const updates = [];

    if (this.newDirection) {
      this.direction = this.newDirection;
      this.newDirection = null;
    }

    const next = this.updatePosition()
    ...
  }

  updatePosition() {
    const next = Object.assign({}, this.parts[0]);
    switch(this.direction) {
      case 'up':
        next.y--;
        break;
      case 'down':
        next.y++;
        break;
      case 'right':
        next.x++;
        break;
      case 'left':
        next.x--;
        break;
    }
    return next;
  }
}

class Game {
  ...
  keydownHandler (event) {
    if (this.snake.newDirection) return;
    switch (event.keyCode) {
      case 37: //left
        this.snake.newDirection = this.snake.direction !== 'right' ? 'left' : 'right';
        break;
      case 38: //up
        this.snake.newDirection = this.snake.direction !== 'down' ? 'up' : 'down';
        break;
      case 39:  //right
        this.snake.newDirection = this.snake.direction !== 'left' ? 'right' : 'left';
        break;
      case 40: //down
        this.snake.newDirection = this.snake.direction !== 'up' ? 'down' : 'up';
        break;
    }
  }
}
...
const snake = new Snake({x:10, y:10}, 'right');

document.addEventListener('keydown', game.keydownHandler.bind(game));