I ensure you that it doesn`t matter if you choose the iPad Air or the iPad Mini with Retina if it comes to Games like HearthStone and similar Games since those Games look on both iDevices great.
If I were you I would choose the iDevice that would fit better your needs:
If you want to use your iDevice more while being on the road or wearing it with you on the way to School/Work I would choose the iPad Mini with Retina instead of the iPad Air since the extra Weight and the Size would probably sooner or latter become a handicap for you if you want to always wear it around.
If you want to use it more as a second Screen to watch Movies or play the newest Shooter also in the upcoming next (two) Years without any hassle I would go with the iPad Air.
Overall both iDevices are great and worth it, it`s just that one might better fit what you want to do with it.