What we are talking about is marriage, not how it is viewed in other countries, but how it is defined in UK/USA.

Not necessarily. Those are just two countries among many. Any changes to how either of them might legally define marriage would only apply inside the borders of the country involved.

I there was an attempt to get the European Court of Human Rights to rule that polygamous marriages that were recognised in Pakistan should be recognised in the UK, but I don't think got anywhere. I imagine the same would apply in the case of same-sex couples from Belgium or the Netherlands - but I would think they'd be recognised as being in civil partnerships, which seems to be a distinction without a difference.