Is having intimate relations by a Non-Jewish man with a Non-Jewish woman who is not married but lives with a boyfriend a form of adultery?
Regardless, it's a despicable act, a breach of faith (assuming the couple had an understanding of monogamy), and very much wrong. Nathan the Prophet tells King David that he did a horrible thing to take away Batsheva from her husband, Uriah. Now in our tradition, it may not have been technically "adultery"; men going off to war often signed divorce papers in case they were never heard from again. But still -- if they had an understanding that they would be a couple if he came back alive, then for David to exploit that is absolutely wrong.
As for whether it is technically "adultery"? Basically we fall back on the Noahide definition of marriage (i.e. what applies to non-Jews) ... which is a little vague precisely because it does not depend on any ritual or outsiders.
Rambam, Marriages 1:1 writes that before the Torah was given (i.e. what was and is the law for non-Jews), "a man and woman could meet in the street, agree to wed, go home and have relations in private, and that's it -- husband and wife." Similarly in his Laws of Kings 9:12 he writes that if a non-Jewish man tells his wife -- get out, you're on your own, or if she just walks out the door on her own, she is now divorced -- no ceremony required -- and allowed to go find another man.
So short answer -- if the "boyfriend/girlfriend" couple still went home to their respective houses every night, they probably weren't considered to be married. If they shared a house ... well I would strongly assume that if they've been in such an arrangement for decades, had children, shared property, and it generally looked like "common-law marriage", just without papers -- well Jewish law would view them as married, papers or no papers.
As far as where exactly in-between would it be called marriage ... it's hard to say. (What's their Facebook status? :) )
Even though such pratices (relations without intention of marriage) are not clearly forbbiden for bnei noah, this is a repugnant act, even if this is done in a provisional time. These are the words of the sefer Sheva mitzvot Hashem on the topic (See SMH, vol 2, Helek 6, 4:11).
Here's a clarification on what is considered "marriage" for non-Jews to be liable for adultery. Rambam Ishut 1, 1:
"קודם מתן תורה היה אדם פוגע אשה בשוק אם רצה הוא והיא לישא אותה מכניסה לתוך ביתו ובועלה בינו לבין עצמו ותהיה לו לאשה."
Before the Torah was given, when a man would meet a woman in the marketplace and he and she decided to marry, he would bring her home, conduct relations in private and thus make her his wife.
So only relations after the mutual decision of getting married make non-Jews married. If either of them has no such intention this does not count a marriage at all no matter how long it lasts and how many kids they have. The very status of "in relations" or "being friends" says "no intention to marry".
If they call it a friendship - they treat it as a friendship, not marriage. If everybody knows that their relationships are a "friendship" they are not married. Once they start to call each other husband/wife - we'll rethink it all. A friend means there's no responsibility to one another - Marriage means responsibility!
This is the reason they have a ceremony in which they both express their intention to marry. Without such a ceremony, the relations alone are not sufficient.