If you wouldn't mind to explain, it seems to me that getting married is a pretty unambiguous statement in favour of monogamy. How does that not change the relationship? Unless non-monogamous people also get married, is that the case?
To be fair, Kat and I were monogamous for a large chunk of our relationship and didn't end up going poly up until we were already married, but here's some ramblings from myself. Also keep in mind this is all US perspective. I imagine a lot of it would be shared outside the US, but not all of it clearly. I also want to clarify that the term Polyamory has kind of changed to be a much more vague term than it used to be, kind of turning into a umbrella term (at least online and especially on FetLife and Reddit) for all forms of consensual non-monogamy while still being used for it's more specific relationship type when necesarry. It can be confusing when reading about the lifestyle, but it's a lot less of a mouth full than non-monogamous.
The easiest way to describe why marriage is still done in the non-monogamous world is pretty much what
Snalin Schimmy said about it, but I am always up for rambling and over explaining. Part of it is just that the concept of marriage has been making another large change over the last 20 years or so. Marriage is quickly becoming, for many, nothing but a secular social/government contract rather than the religious ceremony that it has previously been seen as. A public government contract, declaration and celebration between two people that get to define what it is to them and are allowed to rewrite the vows of said contract when they choose to do so. This happens to be the mindset that we went into marriage with.
Also you get a shit load of legal, financial and social benefits from it. Children are a bit more legally complicated when you're not married, adoption is likely not possible and certain attorney privileges and lots of other things. While there are certainly a lot of poly folk who have philisophical problems with monogamy and/or marriage, there is actually a good sized movement in the poly community wanting Polygamy (multiple spouses with Polyandry being multiple husbands and Polygny being multiple wives) to be made legal. I can't really say I'd be opposed to it, but the nightmare of restructuring our marriage systems, culturally and legally, makes me say that's unlikely.
There are also a lot of different types of relationship within the non-monogamy realm. Open relationships with
Don't Ask, Don't Tell policies (I have issues with the concept behind this),
One Penis Policy (also is a bit of a shit deal to me), Swinging (which actually seems to be dominated by married couples), Poly-fidelity circles (sex only within the group of 3+ people), Poly-Mono couples (one person being monogamous while the other is not, consensually) and many other variations. Some of the relationships will be more serious and some will be nothing but one night stands. It just all depends on the structure that the people involved have agreed to. While it's kind of an unwritten rule in most poly circles to not shame anyone for a "bad" form of poly relationship, as long as it's not actually abusive, as you can clearly tell from my list and how some of them in the chart I'm linking are worded, there are still strong opinions about certain forms of it.
http://i.imgur.com/WBN0O.giftl;dr: Every poly relationship is different and is structured according to whatever the people involved are comfortable with.