with RX 470, u're probably playing at high settings on 1080p on most titles
tbh, the i3 is still good enough, since games todays still uses up to 4 cores anyway... the i3 can still handle another 1-3 years at most imo
if u want a decent upgrade, i would suggest the coffelake i5 / Ryzen R5 instead, or at very least, the i3 8350k, since going from 2c/4t to 4c/4t won't yield as much difference as the i5 / R5 [although game does love real cores rather than hyperthreading, it's not worth it considering the price u had to pay for those new parts, especially with the Z370 mobo, but at very least the i3 8350k is unlocked so u can OC it]
with i3 8350k, u can OC it which means it should perform as good as i5 7600k [which is great enough for games these days] with the cost of less lifespan (since the trend of 4 core already shifting)
with i5 (preferably 8600k) / the R5 however, u're getting 6 core at very least, they perform exceptionally well, and will last much longer because of their extra core count, also, as games starting to utilize multithreading, those CPU will start to show their significant improvement over the 4 cores CPUs
reminder:
Coffelake needs the new mobo (Z370 is the only series available right now)
Ryzen needs AM4 socket mobo (B350 / X370, B350 had better price/features for normal user imo)