I have reasonable suspicion that it wouldn't be nearly as easy to train without "spinning" move which basically gives invulnerability against all enemies sans their bullets, iirc.
I see this videoclip as a great introduction to neural networks and genetic algorithms (something I didn't know existed in ML) rather than a simple "computer completes videogame level". You're probably right nonetheless (I can't remember the mechanics of this mario game) :)
As far as I can tell, it would only require longer time (more iterations) for the network to learn, but it would still work.
The main problem I see is that the algorithm is learning from the same level (or set of levels). It would be interesting to see what happens if you give it some completely new level to play.