Your computer's laptop CPU is too slow to do live x264 encoding. You might try Quicksync, but I doubt even that will work well enough.
The log from last attempt shows network problems:
16:39:27.307: WriteN, RTMP send error 10053 (14 bytes)
16:39:27.308: WriteN, RTMP send error 10053 (54 bytes)
16:39:27.308: WriteN, RTMP send error 10038 (42 bytes)
And render is overloaded in both cases (you need to lower resolution or maybe lower your in-game settings).
To locate the issue - exclude network stuff - make only local recording and playback it on your PC. If artifacts is gone - the issue is in network hardware.
Please, clarify the issue.I lowered resolution in OBS, but am have issues logging into my cam menue. Would it be an older router?