Note it says, " some ".
I'm sure there is more to it than simply persecution of gay couples with children.
Well...the OP article is behind a paywall, but recent moves have been to deny non-biological parents parental rights, and instead direct them to adoption processes.
So, if there was a lesbian couple who got pregnant via IVF (or similar), only the birthing mother would be listed as a parent. To now, there have been no moves to roll back recognition of gay parents which has occurred in the past, so that would account for the 'some' comment.
I'm sure the government isn't seeing it as persecution, but rather than upholding of 'traditional values'. So it would depend on perspective. Surrogacy is illegal in Italy (I believe...it certainly was), so gay male couples going overseas for surrogate procedures is another area which has come under direct scrutiny, and is no longer certified.
Meloni's views seem...well..almost incoherent to me. But I'm certainly not her constituency, so...*shrugs*
But in case you're interested in my views, as a basically centrist onlooker, these are the things I can't square in my mind...
1) Meloni claims her views on children requiring married parents is a result of her own father leaving, and the resultant negative impact on her upbringing.
2) Her parents were married, which didn't stop her father leaving.
3) There is no move to restrict unmarried couples from having children 'naturally', nor to restrict divorce,
4) Meloni is not married, but has a child. She has said she realises this doesn't make her fit for adoption.
5) Gay couples cannot marry in Italy. They can access civil union laws, which are often described as 'basically the same thing' but of course that is completely not true when it comes to adoption rights. It similarly impacts on step-children rights.
6) Foreign gay marriages are not recognised as marriages in Italy, but only as civil unions.
So..yeah. I struggle to combine those 6 points into anything that isn't persecutory, to be honest. Point 6 is actually in breach of a ruling by the European Court of Human Rights. But, gay people having kids isn't 'traditional', so a lot of people will feel better that it remains that way, at least in certain countries and demographics.