How to transfer a music video from MacBook Air to iPod Classic 6th generation?

You do it the same way it's always been done.

Plug the iPod into the Mac using its charge cable, you'll need a USB-A to USB-C adapter.

The iPod should appear in Finder on the Mac's side bar assuming the option for "CDs,DVDs and iOS Devices" is checked in Finder Menu ➜ Settings ➜ SideBar.

Click on the iPod on the side bar and to open its summary page. Then follow the steps in the link below to sync the video.

click here ➜ Use the Finder to sync your iPhone, iPad, or iPod touch with your Mac - Apple Support

Make sure the video has been imported to the Apple TV App on the Mac and is visible under Library ➜ Home Videos or is stored in the Photos app and choose the relevant section to find and sync it.

If it's added to the Apple TV app, you can select the video form Home Videos, and then go to File ➜ Convert ➜ Make iPhone or iPod Version.

It won't say anything once you select the option. Just back out to the home videos listing and the new version should appear in the listing. You should be able to sync that version to the iPod.

That looks like an episode from a TV show, which would normally be DRM protected, if so neither the iMovie nor the TV app options will work for that.

You would need a 3rd party app that can break that protection and we cannot help you with that.

Content from the Apple Music subscription service, be it music or videos, cannot be transferred to old iPods.

Not sure what the CD drive has to do with anything, unless the video is on a CD you have and you want to extract it from there.

If you have the video on your computer already you can transfer it to the iPod. A CD drive is not required.

If the video is somewhere else, then you need to transfer it to the Mac first in some way.

You should not need to convert it. The iPod should be able to play mp4 files just fine.

You may need to resize it though and change its quality for playback on an iPod.

Easiest way is to use Apple's iMovie app (free from the App Store) . Import the video into iMovie, add it to a project timeline by dragging it from the media section and dropping it on the time line, and then go to the File Menu ➜ Share, select the File option, and then choose the lowest resolution (540p) and low or medium quality.

Youtube video:

https://www.youtube.com/watch?v=CbyIJyciN4Y

That suggests it's a protected video. You would need to crack the DRM protection and as said we cannot help you with that here.