We do not use their time stamp.
What time stamp are you using then?
We run a full bitcoin node and use it as the authoritative clock/transaction order
Actually blockchain.info has a very limited api and has gone down many times. We want our system based on the actual bitcoin blockchain, not a third party.
Why use a 3rd party api of the blockchain, when you can use the real blockchain? Take an address and compare the times and transaction orders between blockchain.info and blockr.io. They don't match 100%. We make sure our countdown timer is synched with our blockchain time. The true transaction order/time are directly taken from our node and displayed on our site.
The challenges for the game comes from the fact that the OP is trying to execute a game where order of transactions and timing are critical to the perceived fairness of the game.. Yet not using a common reference (blockchain.info, chain.com, etc.) means users have no external reference to base the game's performance on.. Further the OP even links to blockchain.info TXes so it's reasonable for users to reference it for transaction ordering and timing..
In short the blockchain has no assurance of timing for broadcast or explicit transaction broadcast order but you are running a game that relies on that, and providing users no reference point outside of a self fulfilling statement the server itself is the authority, but your upstream network topology, connected nodes, etc. all have a material influence on how that order works since you are trying to establish it yourself.
Bottom line, if you want to build trust and avoid most of the ambiguity that is inevitable with the current game utilize a blockchain reference (blockchain.info, blockr, chain, etc.) as the authority...
