As the developer, I was going for combining "Snapchat" with "Interception", and "Snapception" was the result. I wasn't even thinking of Inception at the time, an oversight on my part.
The -ception suffix is typically used for nested abstraction; for example running a virtual machine within a virtual machine could be referred to as VMception. This is in reference to the 2010 movie Inception, a major device of which is the use of nested dreams, or /a dream(?: within a dream)*/.