Zazen, which means "seated meditation", is a type of meditation that is central to the practice of Zen Buddhism. It is performed in order to calm the body and the mind in order to gain insight into the nature of existence. The aim is to sit still and quiet, letting all words, images, thoughts, pass by without engaging them.
This is how WikiHow explains Zazen:
"Zazen is more than quiet sitting and can lead to a profound uncovering of hidden awareness within us. This final step is achieved by exploring the stillness we create or discover within us through sitting. Take time to observe yourself and the world when sitting and afterward. Use all your senses. When you acknowledge thoughts as you sit in meditation or go about your day, observe what is acknowledged...and what acknowledges."
Obviously, this practice has nothing to do with Christian prayer which is all about "the raising of one's mind and heart to God or the requesting of good things from God" (Catechism No. 2559). It's not hard to see from the above description that Zazen is not about raising one's heart and mind to God, but about looking within to oneself.
I cannot comment on what was in Maryknoll Magazine because I haven't seen it and the July/August online edition did not include the article you are referencing.
However, I can say that there is great confusion among the faithful, including clergy and religious, on the true meaning of ecumenism, with many adhering to a "spirit of Vatican II" interpretation that essentially allowed Catholics to practice whatever they wanted from other religions provided that it met some ambiguous standard of "good". Of all the practices so freely adopted, Buddhism ranks right up there with yoga as being something essentially harmless. This blog will explain some of the widespread misconceptions about Buddhism and the adoption of prayer forms such as Zazen which you might find helpful.
I'm quite certain the Maryknoll priests are aware of all this, but you might write to let them know how scandalized you were by the article and the nun's behavior.