Your problem is massive overload. And network lag.
17:05:14.623: Output 'simple_stream': Number of lagged frames due to rendering lag/stalls: 9555 (47.6%)
17:05:14.624: [rtmp stream: 'simple_stream'] Freeing 4 remaining packets
17:05:14.630: ==== Streaming Stop ================================================
17:05:14.631: Video stopped, number of skipped frames due to encoding lag: 17210/17674 (97.4%)
16:30:03.513: Output 'test_stream': Number of dropped frames due to insufficient bandwidth/connection stalls: 437 (54.4%)
It looks like you ran the auto-configuration wizard, you specified 60fps and it adjusted your output resolution down to 128x128, and then you changed that to 720p60 and everything lagged completely.
Are you streaming on wireless? Not usually a good idea, and even if your internet connection is capable of streaming at good quality, you may not be able to use it on wireless. It does not look like your connection can currently handle the 6000 bitrate you set as half of your frames are dropping. The drop rate was similar at 3000, which seems to indicate you don't have upload bandwidth sufficient for 60fps content. Set to 30fps.
You've set the veryfast preset. You should probably be at superfast or even ultrafast on your hardware.
Window capture performs very poorly. You will get better results from running shareplay fullscreen and capturing the display.
The MacBook Air does not make a good streaming machine, unfortunately.
