From your logs, the relevant parts here:
Code:
15:43:22.339: Output 'adv_stream': Number of skipped frames due to encoding lag: 8378 (3.8%)
15:43:22.339: Output 'adv_stream': Number of lagged frames due to rendering lag/stalls: 9 (0.0%)
15:43:22.339: Output 'adv_stream': Number of dropped frames due to insufficient bandwidth/connection stalls: 18035 (8.2%)
1080p 60fps is going to be pretty heavy on your system to encode, and it looks like you're just barely overloading things. You might want to drop resolution to 720p, or FPS to 30. Alternate options could be freeing up system resources a bit by capping FPS in the game, or by lowering graphics settings in the game.
For the most part, your video looks pretty decent (if a bit light on bitrate, you generally want 9,000 for 1080p 60fps), outside the parts where your system lagged a bit trying to keep up.