This would be possible using OBS's BrowserSource.
First, find the embed code for the stream (in YouTube you can click "Share" and then "Embed"). Find the src="" and copy the URL that's inside the quotes. In OBS, create a new Browser. Paste the previously copied URL into the URL field, and set the Width and Height to your canvas size (or your preferred size)....
OBS is a video streaming and recording software, not a video player. You will need either find a video player that will play an .flv file, or switch your settings in OBS to record to a different format, like .mp4, which most video players will be able to playback.
The easiest way I think would be to set up a virtual machine. I use VMWare Workstation 12. However Virtualbox is free. Youd have to install your OS and screen capture software (such as Bandicam which I use and recommend) on the Virtual Machine.
But you could run the VM at 4K resolution and use it to record at 4K even on a 1920x1080 host machine without ...
The variable frame rate is all that stands out. Save future videos with constant frame rate. As for these ones, transcode using ffmpeg* to CFR MP4s:
ffmpeg -i currentvideo.mp4 -c:a copy -crf 16 -r 30 -fflags +genpts newvideo.mp4
*Get the 32-bit static build.
You can achieve something which is kind of the same by duplicating the media and changing the transform slightly in multiple times. They have to have color correction and you can tweak the opacity so it looks right. Hope this helps.
I don't believe OBS can live blurring effect. The effect you want is actually called compositing where there are two layers and one does not have a blur effect and the other one does.
Donkey Kong background is actually scaled and blurred.
This can be done in editing but not live.
Check out Blackmagic Design website and look for free editing/color ...