Smartphones to buy under 10K for general use and gaming

A quick comparison between the devices you have mentioned yields the following results -

Display
All the three phones have the similar screens at 5.5 inch size. The resolution is 1920x1080 pixels.
Hardware
Redmi Note 2 is powered by MediaTek MT6795 octacore processor. The other two devices have the powered by MediaTek processors, but Meizu M2 is powered by MT6753 while Lenovo K3 Note is powered by MT67526752. Redmi 2 scores a bit over other two based on having the latest processor.
All of them have 2GB on board RAM. Redmi Note 2 and Lenovo K3 Note have 16 GB internal storage, while Meizu M2 Note is available in two memory variants of 16 and 32 GB. Meizu offers you an expandable memory upto 128 GB while Lenovo K3 Note is capable of just 32 GB expansion option.

Software
Here again, it would be a tie with all three of them running on Android Lollipop.

Battery
In terms of battery capacity, Meizu M2 Note is powered by 3100 mAh battery. Redmi Note 2 carries a battery of 3060 mAh, while Lenovo K3 Note is powered by a battery of 3000 mAh capacity. Meizu takes a little lead over the two competitors.

Camera
There again, the three contenders offer you the similar set of cameras. They carry a 13 MP rear camera and 5 MP front camera.

There isn't much of a difference between the three phones. You can opt for any of them. Meizu has a slight edge due to better battery and memory capacity.
Other possible options include -

Asus Zenfone 2 Laser
Powered by qualcomm Snapdragon 410 octacore processor , the phone carries an internal memory of 16 GB. It has 2 GB of RAM. You get a 13 MP rear camera and a 5 MP front camera. The rear camera features laser auto focus which can focus your subject within 0.3 seconds. Running on Android Lollipop, Asus Zenfone 2 Laser has a battery of 2400 mAh. You can get it on Flipkart at Rs. 9999.

Yu Yureka Plus
Priced at Rs. 9999, the phone is available on Flipkart. Battery capacity is 2400 mAh. It runs on Cyanogen OS which offers high level of customisation. Yu Yureka Plus can also be a good option for your needs.

I am not going for other ones but for the one which we are using at home. It is Xolo Hive, which is gong to give a fantastic gaming experience apart from other general uses.

To make it easy for you I can give you a little description on its specification, in case you find something that doesn't suit your purpose.

It runs on Android v4.4 KitKat Operating System, comes with 2GB RAM, 1920 mAh Li-ion 12.7 cm (5) Displayand has a 1.4 GHz Octa Core processor with 8 megapixel camera with face recognition and many more features that you will love.
When we purchased it was under 10000, but now it has become 12999. But if you can increase your budget a bit, it would give you the experience you are looking for.

But yes even Redmi Xiaomi Redmi 2 is also a good smartphone for Rs. 7,000 for a good Gaming experience. It runs on Snapdragon processor with Adreno GPU that gives the correct gaming speed.

In case of gaming here are three things that you'd need to look out for - screen size, CPU, RAM.

Screen size : Redmi note 2, Meizu M2 and Lenovo K3 note have the same size of about 5.5''. All three of them have IPS displays.

CPU : Redmi Note 2 has Octa-core 2.0 GHz processor whereas Meizu M2 has quad-core Cortex-A53 at 1.3 ghz. As for Lenovo K3 Note, it has Octa-core 1.7 GHz Cortex-A53 processor. However the performance will differ due to GPU aspect as GPU is different for each of it's processor. I'd say Redmi Note 2 and K3 Note have edge on this part.

RAM : K3 Note , Redmi Note 2 and Meizu M2 all of them have 2 GB RAM.

As you can see from the spec comparison, most of the required feature set are pretty much closer. MIUI 7 in the Redmi Note 2 will make the phone more quicker to use due to it's new app cache changes. So the choice is between the Lenovo K3 Note and Redmi Note 2. It's upto you to make the choice between these two phones.

Lenovo K3 note:
Lenovo has recently launched a powerful andriod device which is till now the first rankholder and also the most selling phone now in the market. It offers a superb octa core processor with 1.7 GHz cortex a53 which makes this device lag free, also lenovo is offering 2 gb RAM for multi tasking. K3 note has a huge internal storage of 16gb which can be expanded upto 32gb via memory card, which is enough for you to store all your videos, games, etc.These specifications are enough to make it the best amongst all.

Yu Yureka plus:
With a boom entry of Micromax Yu Yureka previously, made everyone shocked of its performance and value for money. In the same fashion Micromax and Yu launched another device that is Yu Yureka plus, although there is not much difference in both. Yu yureka plus offers a octa core processor with 1.7 GHz a53 cortex. It also offers 2 gb RAM. Rest all the specs are same for Yu Yureka plus and K3 note.

Although andriod devices have come in bulk recently like meizu m2 note, Asus zenfone 2 but the problem with these devices is of the brand which they belong to.

If you are interested in xiaomi redmi note 2 you can also wait for it. As it is coming soon in the market.