It's worth bearing in mind that applications have to be specifically coded to take advantage of threading. With something like graphics rendering it's just a basic buttload of maths to be done in the shortest time possible & you just shovel the numbers in one end and the results come out the other whenever the processor has finished it - speed is important, timing isn't... However with games it's a bit more complex as so many functions have to be synchronised (imagine if the AI, World sim, Graphics, Sound and so on got out of sync!). Also there is a cost in threading things and synchronising them, and you do get to the point where the losses and complexities in doing so more-or-less outweigh the advantages.
Most games producers these days have the sense not to write games that most people can't run well. Since the average processor is a quad and there are a lot of duals still out there nobody is going to write anything for a while that doesn't run well on a quad, and the advantages of more than four cores are likely to be slight for some time to come - because games will not be coded to take best advantage of them. It would just be terrible business to produce a game that the majority of your potential customers can't run.
But, then again, running a single game or program isn't the only point of having a high thread count. On our PCs we have the operating system, the services it's running, we might have things like chat clients, system commanders, fan software, streaming software etc etc etc running as well. So having the opportunity to execute them on a different core to your game is clearly a nice thing and an advantage.
But 16 cores? Well, that makes sense for a server workload, sure. Lots of sessions logged into a server, running lots of applications. But it's a far cry from a PC with a Game and number of minor apps on it running in a single session.
I'll be very surprised if there is much difference in gaming for the average gamer between an R5 and an R7. Probably the R5 will be just slightly worse, but there is also the very slight chance that - for the specific task of gaming - it may be slightly better. It'll certainly be better value! - almost certainly you'd be better off with the top R5 (Which has more than a enough cores for the foreseeable future) than the base R7. Spend anything saved on a better GPU!
Elite specifies a quad-core as it's minimum spec, but people have run it on duals as well to good results.