I agree with you that polyamory as defined at reference.com is as you say. However, if you were to google polyamory, you would see how the termed is generally being used. In its general, popular use, polyamory denotes the lifestyle you mentioned. Also, 'marriage'/covenant is not a requirement for sexual union in polyamory.
I quote from Wikipedia
Polyamory, often abbreviated as poly, is often described as consensual, ethical, or responsible non-monogamy. The word is sometimes used in a broader sense to refer to sexual or romantic relationships that are not sexually exclusive, though there is disagreement on how broadly it applies; an emphasis on ethics, honesty, and transparency all around is widely regarded as the crucial defining characteristic.
The term "polyamorous" can refer to the nature of a relationship at some point in time or to a philosophy or relationship orientation (much like gender or sexual orientation). It is sometimes used as an umbrella term that covers various forms of multiple relationships; polyamorous arrangements are varied, reflecting the choices and philosophies of the individuals involved.
Polyamory is a less specific term than polygamy, the practice or condition of having more than one spouse. (Most polygamous cultures are traditionally polygynous, where one husband has multiple wives. Polyandrous societies, in which one wife has multiple husbands, are less common but do exist.) Marriage is not a requirement in polyamory.
Hence, as Biblical Families, we tend to shy away from the term in order to avoid association.
Regarding polygamy/polygyny, once again the reference definition may say one thing, however, general use may be quite different. Polygamy in general use denotes a negative connotation of immorality in a multiple relationship. Most folks wouldn't know 'polygyny' if it came up and bopped them in the nose.
You will even see on the forums here a tendency to even lean away from the word 'marriage', because of the way modern culture is redefining the term. For instance, the general public and even some levels of government may recognize 'gay marriage', but we would see that as a contradiction in terms.
Personally, I prefer 'covenant relationship', 'covenant marriage', or 'Biblical (not traditional) marriage'.
This is a good question, and one that comes up from time to time as new people enter on the forums. Please know that whatever term you use, we generally know what you are talking about, and if there is ever an issue, we seek clarification.
JESUS IS ALIVE!!
Doc Burkhart