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All Lyin' Ted had to do was to explicitly declare that the article is false
He did just that, explicitly and unambiguously.
...that he has never cheated on his wife...
No, he should not do that since the allegation is not that he cheated on his wife at some unknown time and place with some unspecified persons. He only needs to refute the allegation as made, and he has done that unambiguously. See above.
...and that his lawyers will immediately seek legal recourse.
Maybe, maybe not. Ted Cruz is a public figure and the bar is so high for a lawsuit for slander against a public person, it's hardly worth the expense. When you add to that the the NE never actually makes any factual assertion in its article, but only repeats rumors, innuendo and unsubstantiated dirt passed on from who knows where and who knows who (are you listening Roger Stone?), successfully suing the NE for slander against a public person is very problematic.
It is odd and ironic in fact that it is Trump who has proposed tightening up the slander laws to make it easier for public persons to defend themselves against this sort of crap. And CRAP it surely is.
is it cheating if the wife consents in a power based marriage?
was bill Clinton lying about THAT woman?
No, he did not.
“The article is false.”
“I have never cheated on my wife”
“I will take legal action immediately.”
Seventeen words that have yet to come out of his mouth.
Even a constitutional lawyer should be able to handle that.