“Slå på ring …"—Is this Norwegian hot potato or something? I understood most of the words, but I have no idea what it actually means.
I put a short explanation in the tags of that post, but I can’t blame anyone for missing that.
You’re on sort of the right track, but it’s not hot potato, it’s a Norwegian variant of duck duck goose.
Strike on ring, strike on ring
Strike whoever you want
Strike your boy-/girlfriend* if you want
The one you strike, you strike so hard, so hard, so hard…
The ring in question is the one the players sit in. One player walks around the ring as the people in it sing this. They repeat the bit that means “so hard” until the person on the outside hits someone in the back, who then has to get up and try to catch the first person before they make it around and sit down in the newly opened spot.

So technically, this is a children’s song about violence. Fun!