I know this is going to sound like a very pedantic response, but here are the technical details:
The text you see displayed in VLC are not subtitles. They are closed captions (defined by EIA608). The closed caption information is embedded in the video data itself (not metadata in the container format). Shotcut does not support converting closed caption data into subtitle data. But maybe with some googling you can find a tool that can do it.
I have never tried this, but here is an article that came up in my google search that shows how to extract the closed caption with FFMpeg command line: