Why did Orthodox Christians alter the liturgy of St. John Chrysostom to pray for "Orthodox" Christians?

I'm a Catholic who also attends Eastern Orthodox services, mainly Greek. One of the most bizarre differences between Catholics and Orthodox is that the Orthodox service regularly reminds everyone that they're Orthodox. However, in the liturgy of St. John Chrysostom, both in the "original" Greek, and the translated English, regularly mentions that "we pray for all pious and Orthodox Christians". This liturgy was written some time around the year 400 A.D., at which point the Church was relatively unified compared to today. At least Constantinople and Rome were together. So I think that the inclusion of the word "Orthodox" is unlikely to be original. Furthermore, I noticed that in the ROCOR service which is a "translation" of the Roman Mass, they again added the word "Orthodox", which seems *highly unlikely* to be within the original text. As a Catholic, I was taught in childhood that yes, Christianity has broken up into different sects, but that doesn't make us any better. The Orthodox seem to have taken the exact opposite approach, as the sect-consciousness is *much stronger* there than among Catholics or Protestants. The addition of "Orthodox" may seem trivial, but the Orthodox make a big deal about being the original unchanged church, which seems to be very doubtful to me. I've asked an Orthodox priest about the addition of this word, but he doesn't know, and seemed bothered by the question, honestly. I was very surprised. Why/when/who added the "Orthodox" to the service?