It is sections like 51 and 52 of Evangelii Nuntiandi that often confuse evangelical Christians. What evangelicals call evangelism is here called "pre-evangelism" though Paul VI says that even this first proclamation of the Gospel is indeed part of the larger work of evangelism.
What catholics call evangelism is what evangelicals often call discipleship or simply Christian education. By evangelism Paul VI is talking about, it seems, everything from the first proclamation of Jesus' name to the tribal leaders who have never heard it, to, presumably, catechesis and continuing education for grownups at their churches. The difference is that one view seeks to share the message and secure a commitment to it; the other seeks to deepen a person's allegiance to that message, wherever they may be on a spectrum of spiritual maturity.
We should not be surprised that evangelicals tend to identify that initial proclamation as the act of evangelizing, because "faith comes by hearing, and hearing by the word of God." The fact is that Paul has to explain that this pre-evangelism is in fact part of evangelism: She carries out this first proclamation of Jesus Christ by a complex and diversified activity which is sometimes termed "pre-evangelization" but which is already evangelization in a true sense, although at its initial and still incomplete stage.
Perhaps this tendency to lump in frontier mission (taking the Gospel to where it has never been heard or to where there is no witness to it, like much of the Middle East) with the rather amorphous and all-encompassing term "evangelism" is one of the reasons why the Catholic Church has been so inactive in the Muslim world over the past decades.
It is certainly in line with EN (and Redemptoris Missio by JPII) to affirm a central role for this "pre-evangelism" sort of evangelism in the ministry of the Catholic Church, though I don't know of anywhere that this is actually happening with reference to the Muslim world.