Effective for what? For the purpose of building an athletic body, quite likely not. The exercises are simply not sufficiently taxing if done properly, as they target multiple muscle groups and the only resistance is one's body weight. As circuit training, it falls short in that it's a third of the recommended time, even according to the authors of the paper that's cited as evidence for the 7 Minute Workout.
However, as the saying goes, something is better than nothing, and if done with sufficient intensity (the authors said that it should be at least an 8 out of 10 on a discomfort scale. If you're not sweating heavily, you probably aren't doing it right), it does manage to cram in a fair amount of exercise in a shorter period of time.
On a side note, I've been using the 7 Minute Workout app lately. It's free and adequate to my purposes. The only real caveats I have with it are that the voice on it stutters a little and I needed to install an additional voice package to get it to work. Otherwise, it lets you adjust your intervals and gives you voice prompts for each exercise, the halfway point, and a countdown of the last few seconds.