First thing I would do is increase RAM to 16GB. According to your log, you only have 8GB of RAM. This, to play it safe OBS and Win10 take up about 4GB of memory. That leaves only 4GB to play your games. Minimum system requirements for most games don't take into account that you are running OBS Studio, plugins, etc. in your system. RAM is cheap to go from 8GB to 16GB today (only $60).
Next, offload the CPU and try encoding in NVENC h264 and see if that helps.Your GTX 1080 supports it.
Finally, your CPU is ok to do 720@60fps. I used to have that and replaced it with a much more better system. I could record 1080@60fps with it on a GTX 1060 with games but the quality looked bad. Never bothered streaming at 1080@60fps because it was obvious it wouldn't cut mustard. Given that, I would say it should do 720@60fps but only if you got another 16B stick installed.
To do 720@60fps, I would say that would take at least 4Mbps of sustainable upload speed. if you don't have that kind of upload speed, streaming just won't work. Turn off everything attached to your network (smartphones, other computers, tablets, etc.). Run a speed test and get a number. Then, change the bitrate to be 15-20% less than what is reported (example: 5Mbps reported, set bitrate to 4000).
