In general, no the site is not open source. There are however some games whose implementation is public under various licenses. A few examples:
https://github.com/AntonioSoler/bga-santorini https://github.com/micahstairs/bga-innovation https://github.com/bga-devs/bga-heat https://github.com/quietmint/bga-hardback https://github.com/bga-devs/bga-memoir https://github.com/Syarwin/bga-kingdombuilder
Hm, yeah I can’t think of any from the top of my head. I guess the site’s format works best for euros and the audience seems to be geared towards that too.