From the title of your post, you seem to wonder about the structure of the early church as described in the first sentence of the article. It is broadly accurate, just a bit simplistic.
The Church of Christ is a congregationalist denomination and it is not surprising it would interpret history to suit their church polity.
The Ealry Church
While it is true that each congregation is autonomous, one has to remember that the equivalent of the early congregation today is the diocese. There was no order of priests in the early church - that came in the fourth century or so. Each congregation/church/diocese (and there is one in every town) is headed by a bishop, and as today, he is considered to have derived his office direct from God, not through a central organisation. The first bishops in each town normally would be been sent from somewhere else. Subsequent bishops are usually chosen by the laity and the deacons.
That is not to say, though that each church (they are not called dioceses until much later - they were called ecclesia as in gathering, and I guess congregation could be a valid translation) is totally independent of each other. As brother-successors to the apostles, the bishops do refer to each other and support each other to ensure that the orthodoxy of the faith as taught by the apostles is maintained. The exchanges between dioceses also include letters, prayers, and liturgical books. The letters in the New Testament is only the tip of the iceberg. Many of these letters got passed around to congregations other than the ones they were written to (those guys have a different concept of privacy or authorship than what we have today) and it is not unusual for letters to one church to be read as spiritual reading or at masses in another church.
Gradually, the bishop in the principal diocese in a particular area began to assume greater significance. Due to the greater resource at their disposal, they are able to sponsor new churches (often deacons are sent out to found a church in a nearby town) or support those churches which are not self-supporting. The bishops of the mother church is also often referred to clarify points of faith or practice. Disputes in daughter churches are also referred to them.
Eventually by the 2nd or 3rd centuries, such principal bishops began to assume metropolitan status like they have today, but without the large office staff or palaces. Later, the metropolitans in the three main cities of Christian teaching, Rome, Antioch and Alexandria, began to take on the role of partriachs with jurisdiction over other metropolitans in their regions.
Mediaval Church
Also, to correct the article, after the fall of the Empire, it was easy (rather than difficult as was asserted) for the Church to exert its leadership over Europe as it was the only centre of learning, knowledge and organisation - if that is meant by ‘imposed its will on Europe’. The Church in the East has always practiced a form of Caesaro-Papism (the Emperor is treated as the titular head of the church) even before the fall of the Western Empire and looked to the Emperor for guidance during disputes.
I am not sure where the idea that the Church became more dogmatic from 900 onwards cae from and I think it was rather a romantic notion by the Church of Christ that a bottom-up revolution against an overbearing and distant potent was taking place. What happened was that with the break up of Charlemagne’s empire in the ninth century, different kingdoms began vying for power. Claiming descent from Charlemagne as the first Holy Roman Emperor (counterpart to the Roman Byzantine Emperor in the East), they appointed their own bishops who often take the sides of their monarch during wars with other kingdom. There was no concept of a church of congregants without a bishop.
There was no common language from England to Italy under the Normans as the language of the people (Old English, Old French, various forms of Gaelic & Germanic and local Latin dialects) differed from the language of the court (High French). Latin remained the common language of all the educated class throughout Western Europe. Again, a romantic notion of a small band of true believers eluding the over-powerful Church to bring the true faith to people suffering under the yoke of corrupt clergymen.
