Edit: I realise this is a dumb question but I'm not a homeowner and I've gotten insurance on anything before, what happens if you insure your games and they all get destroyed like this? Do you get a payout for them or something? How do they know what the value is when they're unidentifiable?
I don't know why you quoted me, but it varies from insurance to insurance. Some insurance companies do market value or paid value. Paid value usually requires proof of purchase (receipts). Market value, I don't know how they determine value if they go by ebay or something, but it should be 100% of the value up to whatever your threshold is, mine is half the value of my home, minus your deductible (mine is 2% of my home value I think).
Different insurance companies have different requirements for proof. Some want receipts, some want just pictures/videos of the items inside of your home, some might be fine with a detailed list.
My insurance told me that clear photos/videos that allow all items to be clearly identified plus a detailed inventory is sufficient. I didn't really get an answer on how they determine value, but they reimburse at replacement cost... what it would cost me to replace it.
Though I wouldn't honestly expect any insurance, even ignoring deductibles, to pay out at a rate that would allow you to easily and immediately replace your collection.