YANBU. They need to pay for a proper, official repair or a brand new replacement.
They should also be paying for the lock on your door, which you need to keep their child off your property.
Not the same in terms of value but my Mother once brought my brother's kids to visit and allowed them to ruin a book I'd had since I was a child. I'd saved it in near perfect condition for years because I loved it, eventually with the idea of letting my own child have it.
My Mum saw it on the bookshelf and started badgering me to hand it over. I said no. I said I had other books they could read, they'd brought books of their own. I offered to buy them their own copy, but my Mum had it in her head that my copy was the only copy she wanted them to have and she took it without telling me. By the time I got it back it was ripped, covered in chocolate fingerprints and with dilute juice stains on it.
She would not accept that she had done anything wrong because "It's a kids book, you're an adult, they're kids!" Or, its my book, I had saved it for years because I loved it, it wasn't her bloody book to take and ruin or give away.
Your flatmate sounds the same way, thinking that because it's a games console it's for kids, and because you share a house they have some claim to your stuff and you're being mean not to let her son play with it.
It's not so much what the item is, or what age range it's perceived to be for, or even the value, it's that she allowed her child to take and ruin something belonging to you when she shouldn't have let him near your room or your belongings. It doesn't belong to her, it doesn't belong to the household, but to you.
Ask her how she would feel if you went into her bedroom and scratched something of hers without even asking. Like her phone, or her TV, or her husband?
They need to pay to repair or replace this and teach their child that they can't help themselves to other people's property just because they want to.