The article says they temporarily disable HTTPS to make a call to Flurry, which is an advertising/analytics company. They must be accessing the analytics side.
To be fair to YikYak, they didn't switch off HTTPS, Flurry switches it off by default. Maybe they didn't know of that? In any case, they should enable it and Flurry should make it the default.
I imagine it's disabled by default because at one point in time (not sure if it's changed in the last few years) any application on the iOS App Store using SSL required registration with the US Government for export control.
