The fact that DOMA defines marriage and spouse for purposes of provisions of federal law does not mean that it regulates marriage and intrudes on state authority over marriage. For anyone confused on this point, consider this:
Property law, like marriage, is a matter within state authority. The federal government provides a tax deduction for mortgage interest on a taxpayer’s primary residence. Suppose the state of Massachusetts were to redefine “residence” to include an automobile. Would the federal government be obligated to give federal taxpayers in Massachusetts a deduction for the interest on their car loan? Or could the federal government, without intruding on state authority over property law, define residence for purposes of federal law to exclude automobiles?
Further, from my NR essay, “Federalism and Marriage”:
Congress has often found it convenient to use state-law marital status in federal laws and programs. But it has never accepted state-law marital status as constraining how those laws and programs operate, and there is no reason that it should. For example, under provisions of the Internal Revenue Code, a person who is legally separated from his spouse, but not yet divorced, is treated as unmarried, as is a person whose spouse is a nonresident alien. Likewise, under the immigration laws, a marriage entered into for the purpose of gaining an immigrant’s admission will be disregarded even though that marriage remains valid under state law. How could anyone imagine that federalism means that a state’s authority to regulate marriage for state-law purposes should intrude on how the federal government operates in these and other areas?