To me, the biggest thing he's going to have to do is get WAY stronger. He's a little guy. You don't realize it until you see him in person. By comparison, Nyquist and Tatar look like big dudes. Which, I assume, is because of their respective fitness levels. I don't even really care if he gains weight (which he probably will), as long as he just gets WAY stronger. He's got a really low center of gravity, so if he does put on some muscle and/or add some power, he'll win a lot of the battles he loses.
Other than his shot, there are a few things I really like about his game. He's got good first step quickness. He can jump on loose pucks and find open spots on the ice as a result. He's also pretty defensively responsible. I noticed him backtracking and checking his coverage a lot. Finally, I really like his aggressiveness. He doesn't play pensive, at all. He jumps into scrums, battles on the boards, and will put his body on the line to make a play. He battles, he's just too weak to win the battles right now. But he's definitely not afraid.
He's got an alpha mentality, but right now beta strength. If he can be an explosive 195-200 lbs. (which I don't think is unrealistic given his frame), I think he'll be a really exciting player because he doesn't lack much else.
This is a really good assessment. I think his back-checking and ability to battle for loose pucks have improved greatly. His skating was one of the biggest knocks on him when he was first drafted, and he's clearly improved that as well. I feel like he took the "shoot, shoot, shoot" advice too literally, as there were several occasions where he would have been better served just getting the puck deep. In his last couple games, I think he did a better job with the little things.
The one thing that he probably struggled with (as most guys do when coming up) is not being "the guy". Your total ice time is lower, the offense isn't running through you and you have less time to make decisions with the puck (in part) because you have it less. I think they're going to ease him into the line-up next season much like they did with Tatar. He'll most likely start as the 13th-14th forward, then push to earn more ice time.
As you say, this is going to be an important off-season for him. Pulks has all the tools, he just needs to adjust to the pace of the NHL and improve his strength. He's just going to have to bust his behind.