All the above example are at least BASED on the notion of a man and a women coming together to produce and raise offspring. Eventually that partnership became one of equals just as we began to see all men as equals.
But differing gender is always in the formula.
But that basis has been irrelevant at least since the 19th century, when marriage became defined around love and mutual consent, rather than arranged marriages where love was optional and they were primarily about property alliances and creating heirs to such property.
The sheer fact remains that marriages performed over the last century or so have not been around children. We do not prohibit infertile heterosexual couples from marrying, nor do we sanction fertile heterosexual married couples that actively choose to not have any children at all, not to mention that gay couples can and do have children, in some cases biologically (where one of the partners acts as a "step-parent"--not unlike a large percentage of married heterosexuals) and adoptively, in other cases, as gay adoption is already legal in many jurisdictions, even if gay marriage is not.
In short, your primary argument about marriage being about children is
de facto obsolete on point one, and inconsistent on point two.
Then you define marriage for me (in 10 word or less) and explain why your very arguments couldn't be used by those you would see fit to exclude.
Simple. Based on current understandings of philosophy and the state of Western civilization....
"Marriage is an equal, non-endogamous union between two consenting adults."
Polygamy is excluded for two reasons:
1) As it is currently practiced, it is unequal and abusive.
2) There is no sufficient demand to the contrary.
Arguments on incest can equally be applied to the heterosexual institution of marriage, as first-cousin endogamy was widely practiced in Christianity until recently.
And, as for animals and other inanimate objects, just as they are incapable of entering a legal contract (like children), they are just as incapable of entering a marriage contract (like children).
As for whether this definition can change, the Aristotelian/Thomist "Great Books" philosopher, Mortimer Adler, argued that, "if theology and religion are living things, there is nothing intrinsically wrong about efforts to modernize them. They must be open to change and growth like everything else."