If you pause the film clip at 0:21, you can see a button on the front of the trousers, which was presumably for a second strap that would cross over in an X with the strap he already has on holding up the trousers. So I think one of two original straps was damaged or lost somehow and the lad has just one strap left to use. Why the production details team did this during the making of the film is unclear. But the director may have wanted it.
I once read about an event that someone had observed when Martin Scorsese was filming a scene for one of the many mob films he made (maybe it was Casino). Robert de Niro was getting dressed for the scene and was wearing a necktie with a certain pattern and in certain colours. Scorsese looked at the tie, asked de Niro to take it off, saying he did not think it was right. Then he selected another tie and asked de Niro to put it on. This second tie was identical in every respect to the first! But that's what the director wanted, so that's what the actor wore.
Good clip from the film, by the way. I really like Lee van Cleef in the so-called spaghetti westerns.
I really can't contribute any additional information of the trouser design to which you refer, but that clip, "Breakfast with Angel Eyes ," inspires me to rewatch the movie, The Good, The Bad and The Ugly!" Thanks for that.