Your reasoning is correct. Once marriage is redefined to mean any union, there is no reason in law or logic to exclude any unions, whether they be polygamous, polyandrous, incestuous, or just good friends who want a tax break.
Marriage as redefined by liberal judges in Massachusetts and California now means "any union any aggregate of people wants to call marriage for any reason."
Of course, the only reason to legally recognize marriages is to encourage mating couples to stay together for life. This provides a stable and permanent home for children, and thus a basis for families. Cut loose from its logical foundation in encouraging permanent relationships among mating couples, marriage means anything and nothing.
When marriage means anything and nothing, many mating couples choose to cohabit, and cohabitation is much less stable than marriage. As a result, many more children grow up with one parent, usually a single mom.
These consequences are not simply something I imagined. The decline in marriage and the meteoric rise in illegitimate parenting is already happening in Europe--see the link below.
P.S. For those like Jon who insist that marriage must be restricted to two persons, this restriction only makes sense in the context of a mating couple, i.e., a potential mother and father among whom a third person would confuse parentage. This is not a problem when marriage is redefined to mean any permanent union.