There have been reports to the effect that the E5-1650v3 is unlocked, but nothing official from Intel, as far as I can tell. I don't want to spread misinformation, but it might be worth looking into this. Unlocked Xeons? Yes, please.
https://www.reddit.com/r/overclocking/comments/2ywtko/intel_e51650v3_overclockingyes_unlocked_xeon/
EDIT: But yes, this chip would probably be overkill for you. An i5 or i7 would serve you better in gaming and save you some cash.
Going by this video comparison (8350, 6600K, 4690K, 2500K, 3770K) there should be gains by upgrading your CPU.
But since it's not strictly necessary to upgrade: What about the best-option i5-6600 which is 50 Euro (i.e. 60-ish Dollar, even though intel recommends a 20 buck difference cheaper than the 6600K and has the same turbo frequency. Since you upgrade before you really need to overclock that could be a solution. Not going Z170 but rather (whatever the LGA1151 equivalent of the H97 chipset is) will save you in the neighbourhood of 100 Dollar that can be invested in your next GPU update.
Cost would be around 300$ for the combination of i5-6600 and motherboard. I would do that on the grounds that a R9 290 is not as end of life as the 8320 is (full disclosure: I'm rocking a 8320E, purchased this year, due to need of more power and lack of funds for new motherboard).