Should i buy Lenovo IdeaPhone S720?

This phone is one of the worst you could have picked for gaming. Why? Because it has a PowerVR SGX531 GPU, which is kind of entry level. There are phones with far better GPUs available out there.

I'd recommend you go for Sony Xperia M. It has good chipset and very good GPU, exactly what you need for gaming. It costs ~Rs 12000. Here is a comparison of this phone with a phone having the same chipset and GPU as S720 (this site doesn't have S720 in it's database yet): http://www.suggestaphone.com/phones/compare?phone1=sony-xperia-m-c1904&phone2=micromax-canvas-2-a110 As you can see, there's a huge difference in GPU, and substantial difference in performance.

Other options in Sony/Samsung/etc: Samsung Galaxy Core

In Panasonic: the T11 http://www.flipkart.com/...ybqgtyrjrw if you are constrained on the budget.

In Indian brands, you have lot of options. On SuggestAPhone, go to Search > By Specifications ( http://www.suggestaphone.com/phones/search/ ) Enter your budget range, e.g. 8000 to 13000. Specify 1GB RAM as minimum since you want it for gaming. Dual-core as no. Of cores. And any other specific things that you want (the ones I suggested should be enough). Identify some of them, and use the Compare option: http://www.suggestaphone.com/phones/compare/ Look at the overall performance as well as GPU, and exclude phones where GPU rating is too low.

If you want to do just gaming then you can buy a tab. The reason is you will get a big screen at low price which is ideal for playing games.
The phone which you have described has a RAM of 512MB which is not good for playing games
You should at least have 1GB of ram for smooth functioning of games
I would suggest you to buy a tab instead of a cellphone