ICVT, the company behind JPEGmini
, have announced a similar service for video called Beamr Video
For some interesting discussion, check for instance this post
and the comments in the associated HN thread
I have done absolutely no testing, and have no experience with either service, but to give you a TL;DR of the critique, I think it is that they give the appearance that they invented some advanced encoding mechanisms to improve H.264 and JPEG, while it seems like they are just automatically selecting reasonably good quality parameters for each input and then using a more or less standard encoder.
Now, this is of course not trivial to do either, but the way they are marketing their services means a lot of the press ends up writing it up as "OMG all new super compression algorithm beats everything!".
Also, the impressive results in their examples seems to come from using originals encoded at very high quality which gives a lot of room for compression while maintaining similar quality.