Even I m having the same problem. I m unable to install it from a shared apk file, but it got installed on other Non kitkat android device..
I tried changing the run time to art, deleted every pre installed files of asphalt but all in vein..
Anyone got a solution..
If it's a "shared" apk, then it might work on the other device because it might be designed for it. Not sure about Asphalt particularly, but many Gameloft games have different versions for different processors. That, or you need to make sure you get the game data folder with the .obb in it that goes with the "shared" apk.
But if you are making a clean install from the Play Store, then I'd try to make sure I was on Dalvik (sure, it probably runs on ART, but seems like things install from the Play Store on Dalvik better, in my experience) and like PhilipTD mentioned, if you have had it installed before, delete the game data folder in /data/data and I'd delete the obb folder on the /sdcard in either the /android or /Gameloft folder (I don't have the game and too lazy to Google it), if that didn't get removed either. If all that fails, and you purchased the game, let Gameloft know and I'm sure they could point you in the right direction or discuss a refund.