Perhaps it taps too close to something they were going to do already, like with Nintendo and the fan Metroid 2 remake. Though that's doubtful.
Legal issues can be a silly thing. If people are allowed to get away with unauthorized uses of an IP, then possible precedent is set that might let them win a legal case should an IP holder sue, so often a company just takes action to prove they firmly watchdog that IP.
Usually, you'd think they would wait until someone was trying to sell something, or something was being distributed, like said Metroid 2 remake. This is just videos for something that isn't even out yet (and if I recall, the guy said he would never release it anyway). Maybe WB feels threatened in the sense that the notice this brought will make "Gotham Knights" look inadequate. To be honest, once "Gotham Knights" was revealed to be a Batman-less game, people seemed to stop caring about it.