The game features more affect GPU performance, but OBS can absolutely be CPU intensive depending on how you use it-- how many sources you have, how complex your scenes are, how many scenes you have, which encoder you are using.
16:04:13.106: - scene 'Scene':
16:04:13.106: - source: 'Game Capture' (game_capture)
16:04:13.106: - source: 'Display Capture' (monitor_capture)
Mixing game and display captures in the same scene will hurt performance. Sources stay active and consume resources even when 'hidden'.
16:04:52.852: [x264 encoder: 'recording_h264'] settings:
16:04:52.852: rate_control: CBR
16:04:52.852: bitrate: 2000
16:04:52.852: buffer size: 2000
16:04:52.852: crf: 0
16:04:52.852: fps_num: 60
16:04:52.852: fps_den: 1
16:04:52.852: width: 1920
16:04:52.852: height: 1080
16:04:52.852: keyint: 250
1080p30 with a bitrate of 2000 is... not going to look pretty. If you need files that small, drop to 30fps and/or a smaller frame size, like 720p.
For recording you should generally be using CRF rate control with a value somewhere between 15 and 23. The lower the number, the larger the files and the better the quality can be. The preset controls how hard your CPU works on the encode. So if you have encoder overload, you can go to a faster preset (lower quality, less load) or a lower framerate or a smaller framesize.
I don't see any dropped frames in this log, but it's possible it just wasn't long enough (only five seconds).
16:04:53.177: ==== Recording Start ===============================================
16:04:53.177: [ffmpeg muxer: 'adv_file_output'] Writing file 'C:/Users/theco/Desktop/Videos/2019-01-29 16-04-52.mp4'...
16:04:58.604: [ffmpeg muxer: 'adv_file_output'] Output of file 'C:/Users/theco/Desktop/Videos/2019-01-29 16-04-52.mp4' stopped
16:04:58.604: Output 'adv_file_output': stopping
16:04:58.604: Output 'adv_file_output': Total frames output: 302
16:04:58.604: Output 'adv_file_output': Total drawn frames: 325
16:04:58.604: ==== Recording Stop ================================================