Maybe the videos are missing the headers, my guess.
I don't know of any free video editing software that can handle the .mov (Quicktime, Apple) format (if those files are actual true Quicktime video) so maybe search the web and you "may get lucky."
I've exactly the same problem and procedure, but with a final difference: the recovered video is an mp4 (not a mov). So I recovered all my files, and I can view the photos AND small videos (less than 10mb), but doesn't happen the same with the rest of the videos.
You mean apart from post two? Recuva will recover the contents of whatever clusters are specified in the directory entry, it doesn't check the code held therein. If those clusters don't contain data conforming to a playable format then it will be very difficult to recover the original file data, if at all.
An SD card is probably formatted as FAT32. When files are deleted in FAT32 the directory entry for the stating cluster, and the cluster chains themselves, are corrupted. As we don't know what the OS is, let alone how the deletions took place, or how fragmented the data was, or what Chkdsk did, or how large the files were, it is not easy to offer any advice.