Joe was at Camp David this weekend -- where some of his family members met him to hang out for some QT with grandpa, including his granddaughter, Naomi ... who says she went head-to-head with 46 in a round of Mario Kart -- with both of them in the driver's seat.

Apparently, there are arcade games at Camp David -- and Mario Kart's one of them. Sounds like Naomi's granddad got the best of her. She says, "Secret Service made an exception and let him drive himself!!!!" Naomi adds, "A little rusty but he still won (barely)."

She also posted a boomerang video of herself rolling around in a human-size inflatable ball in what appears to be a gymnasium.

Camp David's got stuff like this for POTUS getaways -- there are stories and photos of presidents past shooting pool, bowling and watching movies in a full theater there on the grounds. So, it's not surprising that they've got neat attractions like this these days.