No, it just means the stones are very pretty.

The expression tou(te)s plus X les un(e)s que les autres is just another way to say très X. The literal meaning is kind of a contradiction — in your example, it would mean that when you looked at any one stone closely, you’d always find it prettier than all the other stones; but the stones can’t all be the prettiest stone. This contradiction makes the expression a little tongue-in-cheek; the literal meaning is not intended when using this expression.