Gamers its not that you have to spend a lot or only high end phones can do some decent amount of gaming, even decent smartphones can do in the mid-range budget.
Firstly lets talk about the processors, now there is a myth that we need an octa-core processor or something like that but that is not true because nowadays if we go for a dual core process or simple quad core processor is more than enough for gaming.The most important thing that we should look for is the GPU that is the Graphic Processor Used on the smartphone.
Now coming to the RAM, you can play decent games with 1GB RAM but to be on the safer side 2GB RAM is what you should look for and not necessary to buy the 3/4 GB RAM models available in the market.
Now coming to the screen size, again its an personal opinion but I feel minimum requirement should be 4.5" screen because smaller screens are difficult to point out on particular points.
Next on my list is the screen resolution, here also you don’t require a high resolution piece, a decent 720p HD screen could do the job for you in place of buying a 1080p or full HD screen. If you are planning to buy a higher resolution screen than you would require a larger GPU.
Another important point I must mention is about the battery life it should be very good, as gaming drains the battery very quickly.
Internal storage should be good as you will store heavy games and requires space.
At the end I would say if you are looking for a mid range budget gaming phone then these specs are more than enough for you.