Yes, they do look like platform hightop sneakers. I would have preferred the sole to be purple as well,but I ran out of the dark color and didn't want to introduce a new one.
The pattern is worked back and forth, one color at a time. The increases only happen every 4th row and are a little fiddly to work (making 6 new stitches out of 1) but results in the pretty, frilly design along the top of the foot. There was a fair bit of sewing to do at end, to close each slipper up from the top of the leg to the tip of the toe.
Pattern is free on Ravelry. My recommendation would be to use a long (longer than 16") circular needle to make these slippers. I used single pointed needles it was a little difficult- the rapid increases create a natural curve to the fabric where the toe is. A flexible cable accommodates this better.
Not a bad pattern- would make again. I saw one modified version on Rav that looks more like a lady's slipper- to sit lower on the foot (less like hightop sneakers). Would require less yarn, as well.