I'm thinking the physical game is where he's having the most trouble. It's a great contrast with Laine since they have a very different way to make space for themselves, and Pulju never really muscled himself into position in FEL instead of just using his speed (which is no longer super amazing when against NHL competition) - speed that seems to be oddly missing as well. The Oilers are employing a more physically oriented style of hockey and it might not be something that comes naturally to Pulju. That could be one feasible context where he's not keeping up with the game plan, getting less minutes because of it and all the problems in his current situation started spiralling from there.
I thought about this as Lucic was interviewed about the physicality of the current Oilers and he mentioned Pulju as well, though adding that he's just 18 for now. In any case, it's clear that he's just looking lost all the time. His positioning is off, when he gets the puck he's just starting to think what to do with it, and when you see shots of him on the bench he's not looking engaged, staring at the replays while the other guys are planning what to do next. Playing like this he would be booted off the Kärpät lineup instantly. Perhaps he's already resigned to that and is only waiting when he can go. I find it kind of weird that the team lets him do this, Mcdavid and the vets should really intervene when it's visible to everyone like this.
I still think he has the potential to become a dominant 1st line winger in any team, he just looks depressed or unmotivated at the moment. Maybe he should call Laine's mental coach? Another possibility to consider is that they're intentionally keeping him on a lighter schedule, since Pulju was known in Finland for being first to train and staying for additional training after the other guys left, and I sometimes thought that maybe he's overworking himself. Though every clip I see from Oilers training, he's just there staring off into space and not looking like he's working his butt off.