Yes they're fat but the fat is deposited differently in the video, it's mostly around the abdomen and main body area whereas in the photo above it's edited to look fat like how people look fat (around the top arms and legs is the noticeable difference). If you look closely at the photo you can see where it's been edited.
The story associated with this is not true. They actually swapped the tiger Cubs with the piglets. There are pictures of the Cubs nursing on a son that are not shown here
youtube.com/watch?v=to7YNCk6zXA