"Are you saying that when I checked out of the casino they added up all my cash-ins and if it totaled $10,000 it would have been sent in?"
Possible. Its what should have happened. But unlikely

I dont know how rigidly they operate things.
Ive done multiple transactions in an LV casino totalling over $10k and asked them if there was any paperwork.
"Strictly speaking there should be, but we know who you are"

Casinos start recording from way under $10k. Maybe $3k? Not sure if it some reg they are following or just 'covering their a$$'. You'd need a casino exec to try and answer that one properly.