I've seen those kinds of articles before, but what I don't see is if they have a recognizable "family resemblance" to western Christianity, culture notwithstanding.
The traditional Christianity of India looks like Christianity as it's been practiced by Christians throughout the Near East and India since it's been there.
I'm not entirely sure what you mean by "western Christianity" if you mean Christianity as generally practiced west of the Tigris and Euphrates then, generally speaking of course. They have their traditional liturgy, they have the Sacraments, they follow Jesus. The most significant difference would be in regards to the Monophysite and Nestorian controversies. I'm fairly sure that they were generally Monophysite (or more accurately, Miaphysite), though I'm not entirely sure on this point. Since the 15th century the Mar Thoma Christians have been split, some joined communion with Rome, some became Protestant, there's one or two that's in communion with Canterbury.
If by "western Christianity" you mean the Western Theological tradition then no it wasn't like it because the Western tradition developed distinctively in Western Europe.
Finally, if by "western Christianity" you mean modern Evangelical and/or Charismatic Protestantism then, naturally it hasn't because modern Evangelicalism is primarily a product of the 19th and 20th centuries.
Have they matured? Have they experienced outpourings of the Holy Spirit/had Revivals? Do they actively evangelize?
They have the Holy Spirit, of course, they're Christians and part of the Body of Christ. Do they preach the Gospel? Of course, though it may not always look like what modern Evangelicals consider evangelism. By maturity, I don't know what you mean. All Christians are maturing in Christ in some degree according to the grace of God leading us toward being more like our Lord.
One article says they had the book of Matthew, with an emphasis on local Jews.
In the 2nd century a bishop traveled there and mentioned that they had a copy of Matthew in Hebrew (which is most likely Aramaic, not Hebrew, ancient Christian writers often referred to Aramaic as Hebrew because they didn't make the distinction). They probably mostly spread among the Jewish communities because, just like everywhere else, the Apostles usually preached the Gospel to the Jews first.
Did they suffer for not having the rest of the NT?
They got the rest of the New Testament eventually, just as Christians everywhere else did. The New Testament didn't just appear, it developed over hundreds of years. If you or I even traveled back in time to the 14th century we'd find that Wycliffe's English NT (like the Latin Vulgate at the time) contained 28 books, having an Epistle to the Laodiceans which managed to stick in the West for a while though being everywhere else regarded as spurious. It was removed by the time of the Reformation, but the point is that the Biblical Canon has been rather malleable throughout history.
Did they evangelize gentiles, as well?
Given that most of the native Christian population in India is Gentile I'd reckon they did.
-CryptoLutheran