The problem with the European Games is it doesn't have the core sports like athletics - the team event has pretty weak lineups - swimming, gymnastics, road/track cycling, etc. which attract the viewers. In contrast it has a lot of sports that frankly British viewers have little or no interest in. Team GB doesn't even bother to send athletes to compete in the non-Olympic sports.
Both the CWG and multi-sport European Championships is a different story and both get full coverage. Personally I thing further development of the European Championships concept is the way forward rather than the European Games but I'm sure views differ from country to country.
To date British TV has never covered these Games and this year it's not helped by having to compete against an Ashes cricket series and tennis's grass court season. It just isn't a fair contest.