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One of my baggage wheel was broken during a trip between GVA Geneva and LAS Las Vegas some days ago. One of its four wheels was ripped of and there was a hole in the hard-case.

My flight was a two-stop trip from GVA to LAS, stopping at LHR London Heathrow and DFW Dalls/Fort Worth.

I reported the broken wheel as soon as I noticed which was at the baggage recheck in Dallas, the employee at the desk told be I had to file a complaint at my final destination in Las Vegas which I did.

I was given the choice to have a replacement with some similar bags they had in the back or take a form to have my damage reimbursed later: I took the form and left without any extra information.

The form is this one, which is linked on AA Delayed or damage baggage.

It looks way more aimed towards lost baggage than damaged one, but nevertheless I cannot figure out what I should have on the last page in the content description and bag row.

Do I have to list my 'old' broken baggage with the receipt from when I bought it years ago, or does this concern the new bag receipt that I will purchase as a replacement?

Note that only the baggage was damaged, no items were missing or damaged but the bag itself.
I have a file number from the complaint I made at the airport and within the 45 days limit so this should not be a problem but I could not find any additional help on how to fill this in properly. Thanks!

This is a form I have filled several times and everything is as you described. To be filled at your final destination with the choice of get an immediate replacement or a repair later. Same as you, I travel with hard suitcases, but none of the ones offered are.

You have to put the value of the old luggage. And of course, they ask for a receipt but sometimes it is nowhere to be found, so you have to leave it out. In this case, they later asked me to give them a link to where the luggage could be bought, something of the same size and brand, although not exact since they changed the models since.

In any case, the value is only used if repair is impossible. The last time I had this happen with AA, they did repair it and I picked it up weeks later at the airport. The time before that, they gave me a voucher at a chosen luggage store in my city.