My first time making cinnamon rolls. I used this recipe from King Arthur Baking Company.
The recipe was easy enough to follow, but they came out a bit flat in the end, despite getting good height off the second rise. The recipe tells you to bake them on a sheet, but I think that was part of the issue with them spreading out. Next time I'll put them in a pan with walls and cram them all together and hopefully that keeps them more uniform.
Yes, they do look very similar to that. And I happen to be Swedish as well, so I think I could speak for the authenticity of that recipe you linked. Just a few notes.
I can tell instantly that this is a very americanized version, just based on the amount of sugar. You really, really don't need that much sugar to make them delicious. You want it to taste like cinnamon and cardamom, not diabetes.
I obviously don't know everything you have in the buns you made in your picture, but to the eye, it doesn't look like there's that high amount of sugar. And you certainly didn't sprinkle yet another layer of sugar on top.
Just do what you already did, and just add the cardamom and the wrapping technique, brush with a beat egg (NOT syrup like they did in the link), and I guarantee they will both look and taste fantastic.