Assuming this is a 'simple' game, like Farmville or Words With Friends, a game where inviduals play for a few moments at a time?
In that case, I'd suggest the classic testing literature - Lee Coplands Book on Test Design and Lessons Learned in Software Testing might help. Personally, I'd be looking at these things:
a) The happy path. Play the game.
b) Requirements. Go through what the game should do - was there anything in there you didn't cover in the happy path?
b) Exceptions. Do things the users wouldn't typically do; do them more than once. I am told that in first-person games that includes things like running into walls to see if you can pass through them, over and over again, and seeing if the physics is realistic enough - for example, when you fall, is acceleration right? If it is, is that /playable/. Real-world rules should give way to playability.
c) Platform. What devices and browsers do you need to support? Come up with a method to test these. You may need to triage and use some logic on what to test how much.
d) Common Mobile Failure Modes. I have written a fair bit about C and D:
http://searchsoftwarequality.techtarget.com/tip/Mobile-testing-tutorial-...
http://searchsoftwarequality.techtarget.com/tip/Software-quality-assuran...
http://searchsoftwarequality.techtarget.com/tip/Tips-for-application-tes...
http://searchsoftwarequality.techtarget.com/tip/Defining-a-strategy-for-...
http://searchsoftwarequality.techtarget.com/feature/FAQ-Testing-mobile-a...
http://searchsoftwarequality.techtarget.com/tip/Android-testing-Expert-g...
http://searchsoftwarequality.techtarget.com/tip/IOS-testing-Expert-offer...
e) Consider something like the test heuristic strategy guide:
http://www.satisfice.com/tools/htsm.pdf
For other things I've left off due to time, space, and attention constraints.
Good luck!
