Yes, the emptying of the mind is the style of oriental meditation. In contrast, there is an old tradition of Christian meditation which attempts to fill the mind completely with one concept.
For example, in the medieval Lectio Divina (http://en.wikipedia.org/wiki/Lectio_Divina), one takes a few words of scripture and repeats them and considers them and ponders them for many minutes. The Cloud of Unknowing recommends doing something similar with the concept of God, or with a simple word such as "love".
This is actually a pretty tough mental exercise to do for even just 20 minutes.
There are two main forms of meditations, with a pretty much infinite number of variations: Concentration based meditation, and contemplative meditation. But it all bleeds together - contemplative practices require a certain level of concentration in order to be able to practice them.
Contemplative practices can range from meditation on a specific subject to general observation of your mind, thoughs, body, environment - this latter form is exemplified very well by mindfulness meditation (vipassana, from Theravada Buddhism, though when mindfulness meditation is taught in the West it is often pretty much cleansed of Buddhist material).
What the article describes sounds close to mindfulness meditation. In this case the goal is to quiet the mind, but not silence it or shut out external impression. The breath is used as an "anchor" that you return to in order to not let thoughts or feelings or observations drag you along, so that you can observe your thoughts in a detached manner, notice them, and move back to the breath.
Compare with some of the concentration practices which include focus on completely emptying your mind for extended periods of time.
I realize that I already replied to this once, but I wanted to make another response not directly related to my other one, and it seemed too lengthly to add as an edit. I apologize if this is frowned upon at HN.
In Soto Zen Buddhism, the point isn't necessarily to "quiet the mind," because that implies that the running rivers of thoughts somehow dry up and give rise to a silent stillness. This may be the goal of some forms of meditation, but it is not the interpretation of Zen.
Dogen Zenji preferred to use the term shikantaza, which means something like "nothing but to hit sit," or less literally, "just sitting." The understanding is that rejecting thoughts is the other side of the coin of embracing thoughts: both are rooted in attachment to the thought, identification of the thought with the illusion of self or ego.
The "purpose" of shikantaza, also known as zazen (sitting meditation), is to neither accept nor reject thoughts. Thus the mind isn't necessarily becoming "quiet," but rather the process of self-aggrandizement is discontinued.
It might seem like I'm nitpicking over your word choice, but Zen in particular is a school that is very focused on how language itself is rooted in the concept of "I" and our ego. You can contrast shikantaza to other forms of meditation that utilize a particular focus, such as an image, which is something that Zen would not generally endorse (for you would simply be displacing grasping at one thing with another thing).
Shikantaza is tied to "thusness," or being fully in the moment, which webwanderings above explains quite well.
When I was in college at the University of Pittsburgh, I took a fascinating class called "Mysticism: East and East" that compared the contemplative traditions of Yoga and Orthodox Christian hesychast prayer. As a practicing Buddhist at the time, it was an eye-opening class.
Now of course Orthodox hesychasm is about communion with a person, whereas eastern meditation is typically not (Pure Land schools of Buddhism are more in line with Judeo-Christian concepts of prayer, though). But I think that there is some common ground for dialogue, and perhaps this paper may be of interest to you or others who enjoyed the original article and are interested in other practices.
There are many techniques that use pure visualization - all in your mind. There are mantra (or prayer) techniques, that require repeating a certain formula, either out loud or silently (in your mind). There are devotional techniques where the practitioner is worshiping an image or a symbol of a deity (the deity itself being a metaphor of some aspect of consciousness states). There are the dancing dervishes. Goes on and on.
From what I've heard so far, meditation is based on focusing on your body in order to quiet your mind. Are there other schools/techniques?