Why doesn’t screen capture videos doesn’t show up in Video app or any other video players in iPad?
Currently there is no way to change the default app that opens a particular file type, hyperlink, etc. 

However, many 3rd party apps allow you to import and/or open photos, videos etc directly from their default locations without first having to transfer the files via iTunes or an online cloud service.

With regard to VLC, if you don't want to connect your iPad to iTunes, then your best bet is to go into the Photos app and save the videos to Files, Dropbox, Google Drive, etc. One saved, go into VLC and access the sidebar, tap on Cloud Services, and then select the appropriate option to access the video.

For example, to access a video capture on VLC, you could:


Go to Photos
Tap the video
Tap on the Share icon and select Save to Files
Navigate to where within Files you want to save the video and proceed to save it
Open VLC
Access the sidebar
Tap on Cloud Services
In the next screen tap on Cloud Services again
Open the video capture