First of all, let's just make this clear because it appears none of you have used Snapchat. THAT WAS NOT A SNAPCHAT VIDEO. He is lying. Snapchat videos have a clock determining the seconds of the video in the right corner. And it was too long to be a Snapchat video.
I don't think he ever said it was a snapchat video
I've never personally used snapchat, but for what it's worth, my wife uses it all the time and once you take a video in snapchat you can very easily save it to your standard photo/video album. It doesn't have any markings. It's not that unthinkable that his cloud account was hacked and they accessed the video somehow.
You might remember last year hundreds of female celebrities had naked photos of themselves leak out on the internet. Keep in mind these are only the photos that leaked out... and only the hacked phones/cloud accounts that actually had naked photos on them. We can easily assume there are hundreds of additional accounts that were hacked into. From what I understand, there's a collection of dorks who brute-force these weakly protected icloud accounts looking for this kind of stuff. Very often, the leaks were actually coming from the boyfriend/husbands of the female stars. The ones of Kate Upton, for instance, came from Justin Verlander's hacked account. It's not a stretch to imagine guys like D'Angelo Russell and Nick Young are targeted because athletes often date famous actresses/models. D'Angelo Russell was recently rumored to be dating Kendall Jenner... that's a pretty high profile name that would make D'Angelo a target from those hoping Jenner sent him nudes.
The site that posts it claims they got it from Nicki Minaj's "people". It was intended to poke fun at Iggy Azalea. Which makes sense... since Iggy/Nicki are about 100x more famous/popular than an NBA rookie and journeyman. So I guess a conspiracy theorist would claim that D'Angelo Russell was the one who intentionally leaked it out to that website. That hasn't been proven, so I don't see the point in judging him for it. If this was simply intended to be part of an internal tank war amongst buddies, it's a bit ridiculous how fans are treating him.
Edit: "Prank" war not "Tank" war. That was a genuine Freudian slip, so I'm keeping it in there.