"My little sister and I play table tennis every day."
Yes, in fact native speakers never use "玩" like this. I play table tennis with Chinese people every day and they will look at you strange of you say this. "玩" is used for playing video games, board games, etc. ("玩游戏"). In this case "打乒乓球" is correct and even DL teaches it that way in an early lesson. Perhaps DL is trying to show the literal English translation here, but people don't say this.
My guess when I saw 玩 was that it was supposed to indicate that "my sister and I" were just having fun with it and not really competing. Like the difference between "leka" and "spela" in my native Swedish. You wouldn't say "leka" table tennis, but if you did, I would asume that you're just hitting the ball back and forth and not counting points (or, I guess, that you were playing pretend and there was no real table tennis at all...). Could this be the case?