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.
I personally prefer iPad mini. But both devices are fantastic. If you want to use your iPad mostly at home, it might be a better idea to go with Air, if you plan to take it with you everywhere, it is better to buy Mini, IMO
I want a widescreen ipad. Like the shape of an iPhone 5. 16:9 is better screen shape than the ipads square boxy screen look. Plus it creates ugly borders at the top and bottom of clips when watching movies and possibly games.
16:9 tabletes are basically unusable in landscape except for games and movies. I have a Nexus 7 which I love and I'd kill for it to be 4:3.