If you want to crowd source anything, it's best to make it as easy as possible to contribute. Having to install a rather unusual language environment, like GAP or PARI/GP, is a boundary that would prevent most people from contributing.
Having an API also makes it possible for more serious contributor to contribute an implementation in different languages. Once you have a few different popular languages (e.g. C, Java, Python, Mathematica), it increases the likelihood that most people will have one of the environments already installed.
Having multiple implementations also allow each implementations to cross check each other. Like most crowd sourced computation project, you need to care about security. It's possible to submit false data, so you want to assign the same ranges multiple times to different people to have a degree of confidence that any false data are going to be voted out by the majority.