Am I reading it wrong? It seems to me that they're adding some gender neutral changing rooms in addition to the male / female ones?
I don't think you are reading it wrong. Unless Primark are building new changing rooms - and I didn't see anything in the evidence to make me think they are - this means re-purposing existing changing rooms to "gender neutral". My guess is that it is women's changing rooms that will be sacrificed. And that they will be next to / mixed with women's changing rooms.
And if anyone thinks that individuals like the cheerful person in the photo are going to use the "gender neutral" changing rooms, they are very mistaken. To do so would not validate their identity.
To make a long story short: men will be using women's changing rooms.