That is a fair question, but it takes too narrow a perspective. The issue is not whether the recognition of "gay marriages" will affect the internal dynamics of marriage as traditionally understood, but whether such recognition would affect the role of marriage in society.
As is so often the case, an analogy is the best way to proceed, and the analogy in this case is with college degrees. A college degree carries with it a number of benefits for the degree holder: the prospect of better-paying jobs, greater respect from society, and self confidence. Wouldn't it be great to extend these benefits to everyone?
Sure, no problem; let them earn the degrees. Of course, that presents a serious obstacle. Some people, due to circumstances beyond their control, are unable to earn college degrees. Maybe there is a way to still be more inclusive, though. There are businesses that will sell degrees "based on your life experience". Presently these are almost all considered worthless, if not fraudulent, but what if we passed laws saying that these degrees had to be treated as fully equivalent to traditional degrees by both the government and the private sector?
The first people to complain would be those who have earned degrees through traditional coursework. Well, what of it? The State has no compelling interest in propping up their snobbish feelings of superiority.
But the State does have a compelling interest in insuring that engineers, doctors, pharmacists, and lawyers have the education necessary to perform their respective roles in society. The fact that those who have earned accredited degrees can make more money serves as an incentive for individuals to fill this role; the status accorded degree holders in society is something the State cannot effectively control and should not even try to, but again it serves as a useful incentive. Yet it has been appreciated for millenia that education has worth in itself, aside from its applications and rewards.
The analogy, like all analogies, is imperfect, but it is also obvious. Just as a declaration by a court, legislature, or even the electorate as a whole can call someone educated without this magically becoming true, no similar declaration can make something that is not marriage into marriage. That is because both education and marriage are more than titles, more than the recognition of society, and more than economic opportunity; otherwise, the State really could award them at will. Both education and marriage have value in themselves, but they also provide important benefits to society, which is why the State has an interest in promoting them and distinguishing the real thing from lookalikes. The benefit provided by marriage is a wholesome environment for the begetting and rearing of children -- the sorry state of many marriages and families and the defects in existing marriage law notwithstanding.