The cost of the gas associated with a transaction is the "amount of gas the transaction consumed" multiplied by the "gas price".
The "amount of gas the transaction consumed" is determined by what OpCodes the transaction uses, and importantly even sending 0 ether to an address uses an OpCode and hence has a small amount of gas associated with it (in this case it was 21272 gas which can be seen in the transaction data on ether scan). The gas price is set by the person / contract initiating the transaction.
The minimum "gas price" that a miner will accept is set individually by the miners, and would generally by greater than 0. However in the beta version of parity (a popular Ethereum mining option) being used at this time (Nov 2016) it was allowed that miners are able to set a minimum gas price of 0.
Hence a whole bunch of these transactions with a 0 gas price were processed. As to who generated these transactions, and why, that is less clear. The only data in the transaction was "0xdeadbeef" which is an obscure "hexspeak" memory address.
These transactions were noticed at the time by the community and a more detailed discussion can be found: