But the clause DOESN'T give Congress FEDERAL power over the SUBJECT MATTER itself. The only subject matter this gives Congress power over is the enforcement of a state to recognize a individual's rights from his home state. The subject matter itself remains a states' issue.
If a state wants to declare that it recognizes a man's "marriage" to five dogs, a mule, a tractor, and the number 23, the federal government should have no authority to stop the state from doing so, but I would suggest that the federal government would be fully within its authority to preemptively specify that the sole obligation of any other state will be to, upon request and payment of such fee as the other state shall specify, not to exceed $1,000,000, give the requestor a sheet of paper bearing the words "The state of ____ recognizes that the state of ____ has declared ____ to be married to ___ [, ___, ___, and ___], for whatever that's worth."