This might just be me, but I really think that really long runs should probably be handled as a relay race instead of a straight marathon.

I think the tacit encouragement that some people might feel to perform runs that are clearly unhealthy, possibly even deadly, is just beyond the pale and not good for runners or communities. I want people to feel free to do tremendous marathon runs, but unless relay as a format takes root, there will always be a competitive incentive for the runner to neglect themselves in single segment runs, and I don't want to wait until someone suffers a heart attack during a 60 hour run to do anything about it.

I'm obviously a little bit biased but, I do recommend Alien Splatter Redux. It's only a dollar, and if your run is deathless, then your playthrough of the main game should only be about 20 minutes or so. It's kind of in the sweet spot for me in being long enough that there's interesting things to do and think about, but short enough that it didn't take me a month and change to develop a solid run.

So, the shortest answer to your problem is that, no, you can't capture audio from just specific windows or whatever, you capture from ¤devices¤, and whatever's being piped through that device is being recorded. The fast and dirty way to isolate the audio of your game is to right click on the speaker in the task bar, open up the audio mixer, and mute everything but your game. You can even mute Windows sounds this way! There is other ways to do this, like using software or separate sound cards to pipe audio to different devices, and having OBS record those devices instead of your headset audio, but I assume you want free and easy instead of things for money that require setting up and reading docs for.

Now, to get to your problem of live mixing, the simple answer is...-don't-! Don't mix live.

Record some early splits to an MP4 while you test out your stream, keeping an eye on your mixer to check your levels (I spring for somewhere between 6-9 DB of headroom on my voice, and 3 DB of headroom between my voice and game audio). Then when you're feeling confident that it -looks good- from just the DB meter, listen to the file (remember to unmute things in your Windows Volume Mixer!) and make sure everything's doing okay. It should sound a bit quiet to you, but that's actually a good thing for boring engineering reasons (most professional audio you listen to has gone through dynamic range compression to sound louder without clipping, there's been an ongoing loudness war in audio processing for a long time, blah blah blah...).

So, I don't see that title listed in the games, which means you need to request the game, and ideally when you do so, you have an attached run of the category already done. That process can take a non-insignificant amount of time, and afterwards, you're now the moderator responsible for verifying runs on that game, and maintaining the page for it. If all of that sounds kind of daunting and a pain in the butt, I would suggest picking something else.

Granted, if you want to run anything...Do it! I think your focus should be on running first, building your skills when it comes to learning games, managing your stream, operating your timeclock, whatever, rather than sweating whether or not you're going to list the best time on a game listed here.