You could argue that if it costs 0.0002 BTC to make a transaction with 1 input, and since one average only 1 in 16 bets will win, the average payout transaction will have 16 inputs making the transaction roughly 16 times bigger and so 16 times more expensive to send.

If all that is true then it is right that they deduct the 0.0002 from the stake amount and not the payout itself. Someone has to pay to "tidy up" all the small bet amounts. The actual number of inputs per payout is going to be pretty random, depending on the coin selection algorithm of the client they are using, but on average there will be 16 inputs per payout.