Precisely
Marriage, in civil terms, is a construct of the government. It is a status bestowed on the basic family unit in recognition of its' importance to society.
A state legislature can create any form of civil union that it thinks appropriate. In the end, they are answerable to the voters. A state Supreme Court (as in MA) has no business in creating new laws.
1. One man, one woman
2. Of a certain age
3. Not of a certain familial relation
("Human" is not specifically mentioned but implied in the "man/woman" context.)
You are also correct that the problem lies with the courts getting involved. However, I disagree that the horse comment is an absurd analogy to make because that is the path that the courts are taking us in making marriage to whoever you feel emotionally attached to a civil right. If requiring one man/one woman is a violation of a civil right, then why wouldn't the other restrictions also violate that civil right? Talk about a slippery slope. I think the gay marriage proponents realize that and the goal is not "gay marriage" but an end to marriage altogether.