No, it's not the same as civil rights or interracial marriage, where a right was being denied based on color of skin. The same argument doesn't apply for that very reason.
If people are in love, what difference does a piece of paper from the state make? No one (as far as I am aware) is suggesting we prohibit gay people from loving other gay people! If THAT were the issue here, I would agree with you, but it's NOT!
No one is being denied any right that others have! It's just not the case here, as much as you want to make that the case! You have inferred your own meaning onto marriage, and based your entire argument on this. What if I defined marriage as being a union between two religious people, sanctioned by a church? Couldn't I make an argument that we should ban all marriage between non-religious people? Most certainly I could, because I have redefined marriage to mean something it simply doesn't mean, and can argue from that perspective! That is what you are doing! Marriage is the union of a man and woman, it ceases to be "marriage" if the union is not between a man and woman.