The words say what they say, no matter how it is spun. Maybe this is a case of bad draftsmanship, maybe not. But either way, this is a dangerous act.
While I think that the drafter's (obvious) intent was to ban "gay marriage", the second clause was to foreclose gay civil unions, as well. However, the words of the second clause would also prevent hetero, single persons living together from, say, having joint health insurance, or joint bank accounts, or maybe even renting an apartment or buying a house. It all depends on what the states deem "legal incidents [of marriage].
Yes, this is probably is in the extreme, but I think we all see that this administration is a bit extreme.