But what IS the church Justin Martyr speaks of???
Most of his works are lost, but two apologies and a dialogue did survive. The First Apology, his most well known text, passionately defends the morality of the Christian life, and provides various ethical and philosophical arguments to convince the Roman emperor, Antoninus, to abandon the persecution of the fledgling sect.
Further, he also makes the theologically-innovative suggestion that the "seeds of Christianity" (manifestations of the Logos acting in history) actually predated Christ's incarnation. This notion allows him to claim many historical Greek philosophers (including Socrates and Plato), in whose works he was well studied, as unknowing Christians.
That makes sense since your religion is built almost exclusively on human philosophy and not actual scripture...
From the same wiki that you linked, comes more that illuminates his actual belief.
Justin had, like others, the idea that the Greek philosophers had derived, if not borrowed, the most essential elements of truth found in their teaching from the Old Testament. But at the same time he adopted the Stoic doctrine of the “seminal word,” and so philosophy was to him an operation of the Word—in fact, through his identification of the Word with Christ, it was brought into immediate connection with him.[28]
Thus he does not scruple to declare that Socrates and Heraclitus were Christians (Apol., i. 46, ii. 10). His aim, of course, is to emphasize the absolute significance of Christ, so that all that ever existed of virtue and truth may be referred to him. The old philosophers and law-givers had only a part of the Logos, while the whole appears in Christ.[28]