This is actually a pretty decent question if you assume that he's not talking about doing any actual gambling himself.

It's a similar question to whether it's ok to own or work at a food establishment that involves serving pork.

You're better off talking to an Imam or Hadith scholar, because the Bitcoin part is much easier to explain to them, than the Islam part is to explain to people here. There are lots of reasonable grounds for nuance and making exceptions due to context, I'm not necessarily sure with respect to behaviors like gambling, etc., but definitely in terms of dietary law and the good intentions of the non-Muslim people you're dealing with in good faith.