Well actually in your log file you have some encoding and rendering lag:
4:02:45 PM.191: Output 'simple_stream': Number of skipped frames due to encoding lag: 1962 (5.8%)
4:02:45 PM.191: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 749 (2.2%)
It's significant enough. 5-8-ish percent of your frames are skipped/duplicated, so your stream probably appeared like it was jerking or had low FPS. Your CPU is getting to be quite aged, and you're decoding the elgato 720p 60fps signal while encoding another 720p 60fps signal. I feel like an upgrade might be in order, especially for that CPU, though I hate having to tell people that because it's obviously not something everyone can do very easily.
If it's just the regular HD or HD60 and not the HD60 pro then that's most likely the problem.
You're capturing a console or different computer with the elgato right? You definitely should not be using that if you're just capturing the same machine, that would be bad. Just have to make sure though.
As for you Zik Maker, didn't I see you on another thread? Could have sworn I responded to it. Let's talk there if you did so we don't derail the original author of this thread.
