real-time video encoding is VERY computationally demanding.
And you have an ultra-low power CPU (the U in the model #) that is 4 generations old, optimized for battery life, not the computationally demanding task of real-time video encoding. And some games don't play nice being captured (not a gamer, so I don't know the details). and in case you hadn't noticed, You logs show encoding lag with the settings you've chosen.
I recommend monitoring hardware resource (CPU, GPU, RAM, etc) utilization [for ex. using Task manager’s Performance tab and/or Resource Monitor] to see if your system is being maxed out with your settings (which I'm sure it is). If you system is near maxed out before even starting OBS, then you will have a problem. I suspect you are going to have to learn how to optimize your OS to reduce background system load, then make sure unnecessary processes aren't running, and then how to optimize OBS
Hopefully your laptop supports NVENC for GPU encoding offload from CPU (or Quicksync for the Intel GPU)... sorry not my area of expertise so not sure if that is what you logs is showing
from
https://forums.developer.nvidia.com/t/nvenc-encoding-on-940mx/47995/5
940MX uses GM107 (nvenc supported) or GM108 (nvenc unsupported).
then read about why not to have game and display capture in same scene
not sure this will help, but from
https://obsproject.com/forum/threads/best-settings.140188/#post-514693 @FerretBomb comment #2
...snip..
3) Use the Quality preset, not Max Quality. Likewise, turn off Psychovisual Tuning. Both of these options use CUDA cores, and tend to cause significant problems like encoding overload when it should otherwise not be happening.
and maybe this will help
Boost your stream quality — choose the right encoder! | by Andrew Whitehead | Mobcrush Blog
Get the most out of your CPU or GPU and stop dropping frames Jul 2, 2020 · 4 min read
Hopefully this will help until someone with a more gamer oriented expertise can help