its currently got a 3rd gen Core i5 and 12GB RAM, so not too shabby.
upgrading either/both of those will not improve gaming too much and certainly not in relation to the cost of a 8th gen Core i7.
is gaming still a big part of it's usage?
there's always the SSD upgrade path. almost no downtime with a cloned image of the current system and the best bang for buck, but again, gaming performance may not increase too much.
so that leaves the R7 graphics card as probably your best avenue for attack - but again, what sort of increase are you expecting for the outlay?