Regarding whether this constitutes a "failed state", I'd say it depends on how bad this gets.
Similar to the concept of "peaceful transfer of power", there also needs to be a relatively peaceful maintenance of power.
Politicians, judges and law enforcement are the very people who constitute a functional government. If, going forward, a certain threshold of the "good guys" start to opt out of joining their own governing system (in one of those capacities) for fear of having themselves and their families murdered, then the country becomes a failed state.
How can other countries prevent that from happening to them, especially Mexico's neighbors?