Yes, at least according to the Orthodox Church, the ecclesiastical leadership is Synodal. But Christ left behind an ecclesiastical leadership (John 20:23), and worship of the Trinity is done in a corporate setting (church). Not to say that private prayers are invalid, but as Christ was both fully human and fully divine, he left behind an institution that, according to the Early Church Fathers and tradition, is both also human and divine. The Orthodox Church (as I’m sure you know from your choice of screen name) is NOT a church in which the worship is void of sacraments and only direct person to diety communication is valid. So yes Jesus Christ, as one person of the Trinity with the same substance as the rest of the Trinity, could be said to lead the Church, he also referenced another person of the Trinity, the Paraclete (Holy Spirit) that would aid in establishing the Church. All this is to say that there are divine and earthly elements to the leadership of the Church, and those earthly (ecclesiastical) leadership elements that grouped themselves synodally did so recognizing that there was a first among equals, even back in the earliest days of the Ecumenical Councils. There one person with “primacy” over the Church Sees, but from the earliest stages of the Church, there was indeed a type of respectful leadership in the synod. As the Patriarch of New Rome, the Ecumenical Patriarch would be the easiest to reference in any media communication. Otherwise, we’d have to explain a whole lot of church history to the world every release that’s done. :-)
Calling him the spiritual leader of the Orthodox World is simply misinformation.
It implies a whole series of things that are not true at all.