I would advise that you try a soft reset before sacrificing your data and time in doing a hard reset.
This method will not remove anything at all from your phone and is completely safe to attempt in any problem situation.
Whilst your phone is on:
Press and hold the Volume Down and Power buttons at the same time until you feel a vibration (about 10–15 seconds). Ignore the "slide down to power off" screen.
Soft resetting a phone usually resolve application problems.
However, if after a soft reset, the application still does not show on the application list, I advise you go through the Store, click the ellipsis (3 dots) and click Downloads. Under there, swipe your finger to the left/right to reveal the Applications Installation History.
If the said game does not show on the application history, then I bet it won't be installed in your phone. So you can go ahead and search for it, and try reinstalling it again.
But, if it says its installed: Still in the store and under the application's profile, click on the "View" button, and it will reveal the application in the application list on the phone.
Also, you can go and try checking for the game from under the "Games" Application.
After you have tried everything I have specified, and you still cannot find it, but from the Store and application installation history it shows that it is installed in the phone, then you can go ahead and do a Hard Reset.