I recommend you experiment with the Audio Dance Visualization filter. It won’t do all of the effects from that video but it’s a filter that moves the image of video based on the soundtrack playing. It may give you some effects that interest you.
Here is a video demonstrating the filter:
One thing though: If the music you want to use is separate from the video you want to affect, then you don’t need to export the video and bring it back into Shotcut like the person in the video above did. Just add the filter to the Output track. And if you want it to only affect a section of the video then trim the filter down to the section you want.