"...we automatically delete the content of your Snaps (the photo and video messages that you send your friends) from our servers after we detect that a Snap has been opened or has expired."
Note that the deletion model is different for non-Snap media:
"Outside of Snaps, the rest of our services may use content for longer periods of time, which means those services may follow different deletion protocols. So, for example, we retain your Story content a bit longer than Snaps so that your friends have more time to view your Story."
Disclaimer: I'm an employee of Snapchat.
I imagine that's what they do.
Then I imagine they're "deleted" off of their servers, but not before being copied to another database that they use internally which isn't attached to the original servers directly.
The core functionality doesn't necessarily require the network effect to be useful, unlike Facebook, so there is theoretically less reason to stick around if the monetization ramp-up negatively impacts the user experience.