Images at the top of the page are created using a Nimslo/Nishika camera [1] it's a 35mm 4 lens camera that takes all 4 shots at once so you get that satisfying rotating depth look at them.
It's really a completely different effect to just stitching a few different photos together.
I had a look at the top submissions on the /r/wigglegrams subreddit [0]. It seems that some (including some of those featured in the article) are the more prototypical stereoscopic wigglegram, whereas others are more a stylistic effect.