I know this is about animation, but the voice actor has a hilarious voice too.
Shotcut has a thing called Video Mode, which is basically the native resolution and frame rate of the timeline (project). All source files will be conformed to the Video Mode at export, regardless of their original frame rate or resolution.
In your case, I can step through the YouTube video one frame at a time (with the “,” and “.” keys) and see that frames are being duplicated on a 2-3 cadence… two duplicates, three duplicates, repeat. This tells me the Video Mode in Shotcut was 24fps (or 23.98fps) but then the Export > Advanced screen was overridden to 60fps. This will not work.
As an example, the 60fps source animation will be conformed to the 24fps timeline, which means 36 frames removed every second to drop it down to the Video Mode specification. When the override of 60fps is specified on the Export > Advanced panel, the 24fps timeline has its frames duplicated back up to 60fps, which is why there is no visual difference between a 24fps source and a 60-that-was-dropped-to-24fps source. This is also why both animations show a 2-3 stutter cadence.
The solution is to change the Video Mode to 60fps, then do not override anything in Export > Advanced.