It looks like the OP is aiming for an index of classes that can be instantiated based on a key. How about, define the classes as you normally would, then refer to them in the index...

class animal {
  a;
  b;

  constructor(x, y) {
    this.a = x;
    this.a = y;
  }
}

class dog extends animal {
  constructor(d, e) {
    super(d, e);
  }

  bark() {
    console.log('woof!');
  }
}

const myClasses = { animal, dog };

const myAnimalName = 'dog';
const klass = myClasses[myAnimalName];

const myAnimal = new klass()
myAnimal.bark()

It feels a bit weird, but a solution to this was to split it up into multiple steps. If the super class is declared, it can be referred to in a second step, obviously.

MDN: Class expressions must be declared before they can be used

const myClasses = {
    'animal': class {
        a;
        b;

        constructor(x, y) {
            this.a = x;
            this.a = y;
        }
    }
}

myClasses.dog = class extends myClasses.animal {
    constructor(d, e) {
        super(d, e);
    }

    bark () {
        console.log('woof!');
    }
}

If there is a way to do it in one step, I'd still like to know.