actually, i've tried it recently... practically the same mechanics and design as all the others
I would put it the other way around: other casinos use the same designs and mechanics as Bustabit/Bustadice.
Both casinos have been around for a long time and still have a very high daily waggered amounts (you can check them out at dicesites.com).
Also, very few casinos even offer the features that Bustabit and Bustadice offer, especially the native script support.
Exactly bustabit comes first don't exactly know if the very first one most of the other casinos just adopted it. You will rarely see new successful game mechanics in casino beside of the dice, crash and others.