(a) "Voltage is by definition (Definition 2) the difference in electric potential between two points." No, you are defining potential difference, a concept that can't be usefully applied to this situation.
(b) If there is a potential difference between two points A and B then a test charge taken from one point to the other will have work done on it by an electric field of an amount independent of the path taken from A to B. This is clearly not the case here. If you choose any two points on the ring, positive work will be done on the test charge if you take it from A to B in one sense round the ring, and negative work if you take it in the other sense. The concept of electric potential is inapplicable.
(c) The electric field generated in the ring if we continuously increase or decrease the magnetic flux linked with the ring is, we say, a non-conservative field. It isn't like the electric field due to static charges, which is a conservative field, to which we can apply the concepts of potential and potential difference.
(d) If the ring were made of metal and had a gap in it, then we would be able to talk about the potential difference between the cut ends. This is because mobile charges are urged round the ring by the induced electric field so one end gets a positive charge and the other a negative. These (essentially static) charges give rise to a conservative electric field.
(e) Back to 'voltage'. This is a more general term meaning work done per unit charge on a test charge. So we can talk about the voltage induced in the ring, meaning the line integral of the electric field strength as we go once round the ring. Specifically, this is the emf induced in the ring.