That clause is exactly a forswearing of power not an exercise of power.
"Section 3 of DOMA codifies the non-recognition of same-sex marriages for all federal purposes, including insurance benefits for government employees, Social Security survivors' benefits, immigration, and the filing of joint tax returns."
You can argue that the federal government shouldn't provide any employee insurance or Social Security survivors' benefits, or regulate immigration, or collect income taxes - but if you grant that any of those are as a whole within their powers, you can't then argue that setting specific policies in those areas is outside their powers.
Show me where in the constitution the feds are allowed to define marriage. DOMA is unconstitutional.
Show me where DOMA "defines" marriage.