Hi Erin, welcome to the forum! Even at one year, your basenji is still a puppy. If he's play biting, he may not understand that what he's doing is wrong if there's not a consistent response from the humans. Perhaps you and your parents should talk about the right response when he play bites. In my view, if the human automatically responds with a loud, "OUCH!", and then, tell the dog to "down", "stop", "enough", "off".. whatever your family decides. Then, immediately disengage from playing; for example, if he's on the couch and playing, bites hard…. "OUCH!".... then "Enough", and gently place him on the floor.
Basenjis don't respond well to negative reinforcement! It's very important not to retaliate and hit back, or negatively push him away, because he won't understand the connection. However, if you place him on the floor, or walk away, he will learn that what he did was not proper pack behavior and he will understand, with consistent repetition, that biting isn't good.
Hope that helps! Good luck!
Hugs and roos-