As we know Bitcoin currently has a minimum transaction fee threshold of 0.0001 BTC (10^4 Satoshi). During the process I make analysis of transactions within the recent two years, I found many transactions that has an (input sum-output sum) lower than 0.0001BTC, which is not considered a valid transaction fee (therefore 0 transaction fee).
For example, the tx with ID ef375a852af090f092426c3dc9e8879eef512c338cbf30b83951cff9196c9862   has only 519 more satoshi in the input sum than the outputs, so this single transaction is considered a 0-fee transaction.
My QUESTION is, in the above case, what happens to the difference of 519 Satoshi? Is this still claimed by the miner, or this tiny amount of money simply goes destroyed?

So you mean that if such a transaction is submitted to a miner who is willing to confirm it, this 519 Satoshi will belong to the miner still?
I guess this should sound stupid but I just want details clarified. Thank you.

Yes.  Miners in current times reliably claim as part of their block reward all transaction fees from all transactions that they confirm.

Note, that the protocol does not REQUIRE that the miner claim the entire reward that they are due.  If a miner wants to claim a smaller reward (and be less profitable?), they can do so and the unclaimed portion of the reward will simply cease to exist.

There was a time in the early days of bitcoin where a bug in someone's mining code caused the miner to claim a smaller reward.  Therefore there are slightly less bitcoins in existence than there otherwise could be.

Miners claim their reward by creating a generation transaction that has no inputs and that assigns one or more outputs.

The protocol limits the value of the sum of the outputs in the generation transaction to be less than or equal to the sum of the block subsidy (currently 25 BTC) AND the transaction fees of all transactions that the miner includes in the block.

The sum of the transaction fees of all transactions in the block can be calculated as the sum of all inputs in the block minus the sum of all non-generation outputs in the block.  Another way to look at it is that the sum of all output in the block (including the generation transaction) must be less than or equal to the sum of the block subsidy AND all the inputs in the block.