Earlier quoted context omitted.
No, you couldn't be extradited from Ireland for being gay because it's not illegal to be gay in Ireland. It has to be a crime in both countries. But in general, questions of jurisdiction are complicated. They're settled by courts, not by what people say on the internet.
If it was illegal in both countries, I wouldn’t need to be extradited since I was gay in Ireland too. Assange isn’t being accused of things that are criminal in the UK.
Whether or not the requirement is met in Assange's case is to be decided by the court. There are certainly laws in the UK that prohibit hacking. Anyway, you are wrong in general about how extradition works. People are often, for example, extradited on murder charges.