As far as I can tell it's a real picture. People are defending Biden saying that's the way to hold a baby sometimes. Which I suppose is true, but the mother is clearly holding the baby here, so why Biden thought it was a good idea to grab the child's crotch for the photo is really odd. I highly doubt the mother was like "Hey wouldn't it be cute if I held just one half of my baby and you grabbed him by the crotch to support his other half? Let's do that!"
I don't think this is anything sexual, Biden's choice of where to place his hand coupled with the baby's expression just makes it all the more hilarious.