It's obvious the answer is they accept 0-conf/zero-confirmation, but most likely they do/check these things (since there's few second delay on the video) before the system decide to verify the transaction :
1. Check fee in the transaction is sufficient to get confirmed
2. Check the bitcoin network if there's double-spend attempt
3. Broadcast the transaction to many other nodes to reduce double-spend attempt chance
But, there shouldn't be any problem with double-spend attempt if the "attack" transaction is broadcasted few seconds slower. More info
https://bt.irlbtc.com/view/423.msg3819#msg3819