I have some videos on my iPad, which have gone corrupt somehow. They do not play and say Unknown in the details.
I had taken a iCloud backup of these. How do I force them to be downloaded back to my iPad to replace the corrupt videos?
Assuming your data falls in a category that gets backed up to the cloud, the simplest method is to tell iOS to erase all content and settings. This gets you a clean slate and best chance to address whatever corruption has happened. You might even test things a bit - then wipe a second time before loading your backup to be sure the device itself doesn't need service or to be restored.
Do check very well that the specific videos you seek are getting backed up and perhaps take the device offline (AirPlane mode) temporarily to prevent a backup of the bad data if you can.
If the photo roll is corrupted (which is often the main cause of this), you will need to wipe the entire device as there isn't a lever to delete just that data and the associated files. (Yes, you could jailbreak it and perform surgery or perhaps find a tool to do this, but I don't have the knowledge / time to assist there)
Once the device is empty, sign in and restore your backup.
Here's the problem. Unless you caught the corruption and disabled backup, it's entirely possible the corrupt data is sitting in the cloud. Without a second device, you can't easily test things, so be sure you are ready to erase things. I would take the device to a computer and get a second backup, just in case - but I have lots of other things I care more about than the camera roll.
Best luck - here is the required reading on backups as well as iCloud:
The first is specific about how iCloud is different than USB/WiFi backup to a computer. The second is more general and includes restore step by step guidance.
iCloud does not actually backup the videos, only the metadata. The Videos themselves still need to be synced via iTunes or the App Store/iTunes download on the device.
Like the old backups made in iTunes, the backup contains the metadata, settings and various other bits or pieces that is not part of a normal sync or purchase.
When you restore a backup it will afterwards start syncing the actual media and apps from iTunes, if it is done via iTunes, or start downloading the media and apps from the App Store if you haven't used iTunes for syncing. This does not include videos or music that was not purchased from the iTunes store.
The only videos that are backed up are those in the Camera roll as per this Apple support document. Also note the disclaimer at the bottom: