Yes it does. <edited>
1) FX-6300 is good enough to run games at decent framerates. Not as well as the Skylake i3, but it's absolutely fine to use an FX-6300 for modern games.
2) He can't afford the FX already. If the FX-6300 costs $100, and $50 for a AMD 760 motherboard, that's already out of his budget. It's already 10217 INR. An i3 costs $125, and H110 motherboard runs for about $60. It's another 2400 INR that OP will have to afford. I don't care about how much performance/dollar is at risk here. He called out the budget. I don't wish to raise it when money's hard to grab where he is.
As much as I would care about price/performance in other situations, this is not the case. The budget is low, and the i3 would tip the balance of the build. You still look to tip the balance. You are technically not looking for the benefit of the OP. Posting on this forum is looking to help people, not call out whatever you feel is right and stick it up someone's butt.