There I think they just mean he is doctrinally conservative, i.e., on doctrine he agrees with the hierarchy on the right, and not with the hierarchy in the middle or on the left. It doesn't mean he belongs to a really ultra conservative wingnut Catholic group, of which there are several.

Your question brings to mind the whole "groups" thing for me, I think the Church gets an undeserved rep for always having been a "top down" organization. In actuality, what their history is that they have always done "bottom up," too, with holy orders, and this is where the confusion sometimes comes in for folks who weren't raised Catholic. There's a history of co-option of bottom up peoples' movements with charismatic leaders (like those of St. Francis, St. Dominic, or St. Ignatius with the Jesuits,) they would watch these new groups form, and after a while either reach out to them, make them a holy order, so they were under their control, or label them heretics.  Hence, they also tolerate organizations like Opus Dei.  Right wing, left wing, middle, all okay as long as you obey the pope on doctrinal issues.  They are open to different views of theology and practice that way, they would rather co-opt than have schisms.

Nowadays, the largest influence of the orders is on the teaching and training of priests and nuns, as they run the main seminaries, according to their individual interpretations of the church and their founder's mission and theology. They have different vows, different missions, and different practices, and are all allowed.

The modern church has expelled , and not embraced some conservative Catholic groups that wish to practice 1950's style Latin rite, so they do not always favor conservatism uber alles. Groups are not allowed to reject the whole of Vatican II nor are they allowed to reject the theory of Humanae Vitae.

P.S. To be clear, one can be a priest and not belong to an order, trained through diocesan seminary.

Associated Press article also says his biographer says not a "liberation theologist" or progressive; basically implies just classic Catholic teaching on helping the poor:

.....Bergoglio's authorized biographer, Sergio Rubin.....

....Rubin, who obtained an extremely rare interview of Bergoglio for his biography, the "The Jesuit."

"Is Bergoglio a progressive — a liberation theologist even? No. He's no third-world priest. Does he criticize the International Monetary Fund, and neoliberalism? Yes. Does he spend a great deal of time in the slums? Yes," Rubin said......

I'll read them both. But this related just popped up on a NYT menu so I'll add it to our communal reading list:

A Catholic Comeback for Latin America? March 14

It's a "Room for Debate" feature with 5 different expert essayists.

This is the essay that caught my eye as being most on topic of what we are discussing, but it appears she might be offering somewhat of an alternate analysis:

Catholicism’s Secret Weapon

Virginia Garrard-Burnett, author, "Protestantism in Guatemala"

Pope Francis's election may be a good start. The church also has the Virgin Mary. Some who stray and return feel that Protestants just can't compete.

....What else can the Catholic Church do to compete with the appeal of Pentecostalism in Latin America? The church has several options.

The first is to try to beat the Pentecostals at their own game, through encouraging the growth of “Catholic charismatic renewal,” a type of Catholicism popular at the grass roots that in some ways mimics Pentecostalism in its exuberant worship services, speaking in tongues and other lively displays of the “gifts of the Holy Spirit.”

A second option takes the inverse approach.....

I want to throw in this thought before I read it: that Catholic missionaries used to be (centuries ago) the champions at co-opting indigenous spiritual themes and practices and incorporating them into local Catholicism. They are the main reason not only for the huge size of the church but also behind a lot of the cross-cultural stuff we have before there was international mass transportation.

(She is right to point out the Virgin Mary. For example, Our Lady of Guadalupe has a hidden layer of coded messages for the indigenous people of Mexico which goes a considerable way towards explaining her popularity.[31] Her blue-green mantle was the color reserved for the divine couple Ometecuhtli and Omecihuatl;[32] her belt is interpreted as a sign of pregnancy; and a cross-shaped image symbolizing the cosmos and called nahui-ollin is inscribed beneath the image's sash.[33] She was called "mother of maguey,"[34] the source of the sacred beverage pulque,[35] "the milk of the Virgin",[36] and the rays of light surrounding her doubled as maguey spines.[34])

The church has lost its skill in doing this, mho. Attempts at getting some "charisma" would be getting back on the old path.