I glanced through the recent signatures when I was signing, and the vast majority are Swedish.
Since airsoft is played in multiple countries, it doesn't hurt for lawmakers in Sweden to see the opinion of people who currently live in countries that do legally have green gas weapons.
When making municipal bylaws, you would probably look to other municipalities that have passed similar bylaws, to see how it went over there. If you're passing a provincial law, you'd consider what happened in other provinces. If you're passing a federal law, it couldn't hurt to see what similar laws have done to other countries.
But in this case, I think it's really just about the numbers. The vast majority of those who signed are Swedish. Having 10% of the 1000+ signatures coming from international players won't make the government look at it, and say "pah, it's foreigners trying to influence our laws". They'll just look at it and say "here's a signature with 1000 signatures".