From your log:
02:02:00.827: [game-capture: 'Game Capture'] d3d11 memory capture successful
02:02:00.827: [game-capture: 'Game Capture'] memory capture successful
[...]
02:05:22.434: [game-capture: 'Game Capture'] d3d11 memory capture successful
02:05:22.445: [game-capture: 'Game Capture'] memory capture successful
[...]
02:11:16.014: Output 'simple_stream': Total encoded frames: 34146
02:11:16.014: Output 'simple_stream': Total drawn frames: 34148
02:11:16.014: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 1026 (3.0%)
This looks like a graphics/rendering issue rather than a streaming issue, though it's hard to say because the log is missing some information at the end of it.
Do you have the "multi-adapter compatibility" enabled in your game capture source? If so, try disabling it. So long as OBS and Overwatch are both running on the same graphics adapter (presumably the GTX 1070), it should still capture just fine.
When you make a new log, be sure to stop your streaming session, exit OBS completely, and then re-open OBS and select "Upload Last Log File" (Help > Log Files > Upload Last Log File). This should provide us with important data on how OBS performed during that session.
