Video transfer

You have a variety of options to transfer files.

1. You could upload your video to a cloud service, eg. iCloud and download the file onto your iPad using the files app. I frequently do this at work to go from PC to iPad. Google, dropbox, etc will all work too.
2. You can connect and transfer files through iTunes, https://support.apple.com/en-us/HT201301
3. You may be able to transfer using an external drive and dongle connected to your iPad too

It would be if you synced the video from another device. The fact you moved the video from another device, it puts it the same as synced photos, they are in a separate album, but synced movies go to the Apple TV app.

The only way is via iTunes. Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support

The Apple TV app is the app on the iPhone to watch those videos that come from other devices. I'm sorry you weren't fond of it, but that is how it works.

You could also just directly upload the file into photos at iCloud.com. That would serve the same purpose and update any connected device (to that account) without all the other pieces.