What benefit is there to playing highly repetitive games?
Lumosity has a research section that explains how their repetitive games help in day-to-day activities. They claim it's peer reviewed, although all of the papers are published to their site. 

However, Science based medicine had this to say about a study with games similar to Lumosity...


  This one study, of course, is not definitive. It is possible that more training is needed before significant benefits are seen. Perhaps
  video games are more effective because they are more engaging and
  players will spend more time playing.What this study shows, however,
  is that products sold as brain training games had no documented
  benefits after six weeks of use.
  
  Putting this study into the context of the overall research, it does
  make us more cautious about concluding that there are general
  cognitive benefits to brain training games or entertainment video
  games. Benefits are likely to be closely related to the specific tasks
  involved in training, and not transfer to unrelated tasks.
  
  But there is already enough published evidence showing visual
  tracking, multitasking, and executive function benefits from action
  and strategic video games respectively that this study will not be the
  final word. When there is conflicting research, more study is needed.
  
  This study is most applicable to brain training products, and shows
  that the marketing claims for these products are not justified. There
  is very unlikely to be any benefit, or any specific advantage, to
  “scientifically designed” brain training applications. For now, you
  are better off just playing a video game.


So, more or less, there isn't any information suggesting that these repetitive "brain games" actually help develop skills outside of learning to play the game better.