I can't find the original La Repubblica story it's supposed to be based on. However reading the story in Italian it would seem the basis for a criminal charge appears to be a form of verbal domestic abuse.
He can whine about the housework and cooking all he likes, but it looks like the claim of constant verbal abuse is what the denuncia stands upon.
I've lived here for 20 years, if women got banged up for being crap at housework and cooking I'd have starred on "banged up abroad" by now.
Is Italy the least mysoginistic place on the planet ? Nah. Not by a long chalk. But are those of us here at risk of imprisonment if we don't Stepford wife to our husband's prefered standards ? Nope.
I'll look out for sources with more detail, but I do rather expect this to be something of a storm in a teacup with the crux of the matter being rather different to the strap line.