I agree. The pictures make him look narrow through his flank, but he looks quite healthy in the video... I wish I could offer more help.
His ribs don't seem to be showing. He just seems a bit narrow through the flank and hips. I would maybe be less concerned about putting fat on him and more concerned about building up those hind muscles. I think he'd look lovely with more muscling on his butt.
Though, I'm no thoroughbred expert, I deal more with stock type horses, so someone on here may want to double check me. ;]