From what I’ve read, his first wife ASKED for the divorce.
But as I understand it, a divorce, whoever asked for or may have caused it, would be irrelevant to the Catholic Church. They have to get a church annulment. So far as I know the Catholic Church is the only Christian denomination that even has annulments, tho some states annul marriages civilly. The latter could, I suppose, be converted to a Church annulment, or certainly give grounds for a Church annulment.
The church annulment process is fairly controversial, I know. But I am pretty sure both parties have to agree to it or it’s a no go. Or, at best, pretty ugly, much like so many civil divorces. That was the situation my brother in law faced, the refusal of #1 to agree, ever, to an annulment. Apparently Mrs. Gingrich I agreed to the annulment as well as civil divorce of their marriage. And therein lies the difference.