The idea is that in the long term as the block reward tends toward 0, the value of bitcoins rise and a tiny fee from each transaction compensates the miners as much or more than the current block reward does which will continue to incentivize them to be honest.
Currently, fees are essentially an anti-spam measure to keep people from creating millions of transactions with the same coin and DDoSing other transactions. I.e. without fees a single person could be issuing more transactions than this stress test did, for free, non-stop.
Dogecoin has the same thing. It was likely not free for you to send those coins (unless it was an off-chain transfer via a hosted wallet [think transferring money between checking accounts at USBANK])
Although, a hostile party would be able to stop transactions without fees from being processed simply by flooding them.