Well what I do see from your prior log that you had it running on the nvidia at least once, but other cases you had it running on the intel. Maybe the game is sometimes running on the intel as well, I've heard reports of that happening as well. Argh I can't stand laptops sometimes. Or maybe the problem could be that it's one of those optimus' or something. I'd probably have to be on the actual computer to know for sure, but I'm pretty sure that yea, the only way you can set up those god forsaken things to capture properly is by using the control panel and by setting your video adapter in OBS' settings to the very top one in the list.
Other than that, if you still have problems and don't really want to bother with it, the only other way is running the game in borderless/windows and using window capture with compatibility mode checked. It will force a cross-adapter capture.
I know these laptops can work with the proper capture though, and I know it seems like a pain that you have to deal with this, but the fact is that the most efficient type of capture is when OBS and the game are successfully running on the same graphics adapter -- It will incur the least system resources and the least system bus transfer doing so. I wish there were an easy way to just auto-detect everything to do this but there doesn't seem to be a way to do that programmatically, otherwise I'd do it so users such as yourself didn't have to jump through any of these annoying hoops.
Laptop manufacturers designed laptops this way for power saving, there's little I can do about it unfortunately.