The original comparison was an i7 7700 (non-k model) vs an R7 1700. Both are valid gaming processors. Will an i7 7700 (non-k) beat an R7 1700 in a drag race when it comes to gaming? sure. are you going to notice the difference between 100 fps vs 80 fps at max settings at 1920x1080? doubtful. at 2560x1440 they both provide roughly the same fps as the gpu becomes the bottleneck at that point. Streaming, the R7 1700 provides a better experience. My personal issue with the i7 7700 (non-k) and the kaby lake platform in general is it is a dead socket. there are no further upgrades planned for it whereas with AM4, you are good until 2020. that means you can get a ryzen today and in a year put in a ryzen+ or even possibly a ryzen 2 in it without having to completely overhaul your core system.
At the end of the day, either processor will provide an enjoyable experience, however one socket is EOL and the other socket is just beginning its life cycle