It sort of depends on what you think Snapchat does. If you think it's
temporary photo sharing, who knows. If you think it's
expiring content sharing, there's been imageboards and textboards forever. Given that Twitter "expires" content off your stream and off your own profile after 3200 tweets, Twitter could be considered that sort of model. You can probably imagine how you could make a custom Twitter client that works like Snapchat but uses Twitter as its platform. You might wonder if there'd be a market for that.
But all of these over-simplify and over-generalize what Snapchat does. The correct answer is #4, the one you couldn't envision.
If you were surprised, it means you don't understand why people use it, which means you're not thinking of it in terms of the problem it solves for them, but only as an idea with an arbitrary, coincidental implementation.
Snapchat solves a problem for a segment of users and solves it very well. It is both a solution and has a well-executed design. You need both, and then you also need marketing and network effects and traction and luck.
To better understand why Snapchat is the current communications darling, you might look into danah boyd's research into how teens use social networks, or this recent anecdotal exploration of one US 10th grader: https://medium.com/product-design/d8d4f2300cf3
Don't start with an idea, start with a problem that you have evidence exists, then develop a solution.