It's because he doesn't play on the PP for Frölunda.
As far as I know Montén (Swedens head coach) hasn't made a comment on this specific case, and I'm not saying that he is right or wrong, but he has mentioned it earlier that, since it's such a short tournament he prefers the players to have played the specific role for their club, so that they are used to it, and doesn't have to learn while on the job.
Also, just a personal opinion, but I think the weaknesses that are still there in Edvinssons game (passing and shooting accuracy) lends itself quite poorly to playing on the PP. Edvinssons strengths in the offensive zone is that he is very mobile and unpredictable, where he is opening up a lot of space and creating holes in the defense by moving around (and his pinches). None of that is particularly useful on the PP though, making tape-to-tape passes, being there as a shooting threat while also being open as a safety net if the forwards are getting in trouble are the primary requirements as a PP "quarterback". Not saying he will never get there, but at the moment i don't think he has the accuracy to full-fill the PP quarterback-role, and I think that's one of the reasons he didn't get an extended look for Frölunda.