They are clearly the simplest Latin chants, adapted so that the English can fit into the Latin meter. The result is not terribly natural for English singing (particularly not when compared to English plainchant!), but is singable enough, and the non-Latin-scholars in our group had little difficulty with it.
Coming to these from a Latin chant background was an interesting experience. Many of the chants are modeled on the Latin - which means that they are similar, but not exactly. The most noticeable difference is that any note that was lengthened - whether by a horizontal episema, quilisma, or bistropha - is no longer lengthened (try singing the Sanctus giving all the notes the same metrical value - phew!)
But the Gloria, the Creed, the various responses - these are all based on the Latin tones. Again, not the same, but based on. Even the tone for the Lord's Prayer and its doxology is not the familiar one but the Latin one!
So I can't help but wonder: Why? Is it possible we've set ourselves up so that English-speaking congregations around the world will be able to easily learn the Latin tones in 5-10 years, as Rome has been asking of us for decades?* The Latin (or Greek, as the case may be) to the same tone is printed below for the Kyrie eleison (Lord, have mercy),** the Gloria in excelsis (Glory to God in the highest), the Lord's Prayer,*** the Sanctus (Holy, Holy, Holy), the Agnus Dei (Lamb of God), and these parts are always referred to in the GIRM as I've recreated them above (as opposed to the current translation, in which only the Latin name is used).
Of course I don't like everything about the musical notation (two syllables for Bap-tism in the Creed is vying for first place), but it's cool to see: as the English-speaking Catholic world is being given words that reflect in detail the Latin of the editio typica, we are also being given chants that similarly reflect the Latin ones in our tradition. Would that I might see the day when Catholics around the world can actually sing a few unifying pieces in Latin!
Cantate Domino canticum novum laus eius in ecclesia sanctorum!
*Pope Pius X asked for this in Tra le sollecitudini (par. 3) in 1903; the Second Vatican Council mandated it in Sacrosanctum Concilium (par. 54) in 1963; and Pope Paul VI sent a booklet called Jubilate Deo to every bishop in the world with "a minimum selection of sacred chants" (letter here) in 1974. Other examples exist, but I find these both most important and most compelling.
**The Kyrie is sometimes just called the Kyrie. I haven't managed to figure out why this one gets to drop its translation, but none of its brethren do.
***The Lord's Prayer, like all the others, is given first in English, then in Latin, to the same tone. Of note: the doxology after the Lord's Prayer ("For the kingdom") is only given in English, though it, too, is to the familiar Latin tone.