My pure guess, but I think vinnartåg means the red carpet where the winner and celebrity walks.

I checked some other sites where the term is used , e.g. in sports. It suggests you go from one win to another, thus, a winning streak

Although "string of wins" and "winning streak" are correct in terms of summing up that the film has been a great success, with one win after another at various festivals (, plausably in an unbroken line), they don't capture the sourcetext's way of describing these wins.

The term "vinnartåg" is not common usage, but derives from the more common term "segertåg". "Tåg" in "segertåg", in turn implies a sort of parade, march or campaign with military indications. Nowadays the usage of this term has widened and is actually more commonly used in sports, businness, art or any other area when one wants to describe how a phenomena conquers all "as if it was an army". In my opinion, The English "victory march" captures this quite well.

"...with its many triumphs on international film festivals..." would probably be how I would translate it.

Den gamla översättningen av svenskans "segertåg". En aning pompöst kanske, men varför inte?!