Born in the Long Island town of Syosset, N.Y., Nystrom is the son of Bob Nystrom, who won four Stanley Cups as part of the New York Islanders dynasty in the early 1980s.
Back in New York to spend time with his parents, who still live on Long Island, Nystrom told NHL.com during a visit to the League's office in Manhattan that "there's a little buzz going on" about the Islanders.
The eighth-seeded Islanders, in the Stanley Cup Playoffs for the first time since 2007, won Game 4 to tie the top-seeded Pittsburgh Penguins 2-2, meaning there's a guarantee for an elimination game Saturday in Game 6 at Nassau Coliseum.
"Pittsburgh was supposed to dispose of them in four straight easily," Nystrom said. "There's a little buzz brewing about the Islanders now. Might be because I'm here and my parents are going nuts [but] there's a little buzz going on."
Nystrom said his father and other members of the Islanders championship teams are pleased to see something nice building with the franchise after so many down years.
"I just think that they're excited to see the team having success," he said. "Being in the playoffs and being in this series is great for them. They've been through some downs. There was that period where everyone was making the Islanders out to be the laughingstock of the League. Now they're in a good situation and they're playing well and it looks like they have a foundation to be a solid team. And I think they're proud of that. They wore that logo and they wore it with excellence. To see it coming back and making the playoffs, which is tough to do, and playing well, I think that means a lot to those guys."
Nystrom is hoping for a return to the playoffs himself -- he last was there in 2009 as a member of the Calgary Flames. He had 11 points in 48 games in 2012-13, but the offseason additions of veterans Jaromir Jagr, Derek Roy and Ray Whitney wasn't enough to get the Stars back into the postseason. After going into the last week of the season with a shot at qualifying, the Stars finished 11th in the Western Conference, seven points out of a playoff spot.
Playing with Jagr was a personal highlight for Nystrom, who said he had Jagr posters on his wall as a kid. Nystrom said he even got to play on a line with Jagr at times last season.
"We call him Jimmy -- that's his nickname," Nystrom said of Jagr. "He'd be like, 'Give Jimmy the puck.' And as soon I got it, I would give it to Jimmy and go somewhere and the next thing I know it's on my tape.
"It was a pleasure playing with him."
Nystrom said it wasn't easy seeing Jagr, along with a few other veterans, leave ahead of the NHL Trade Deadline, but the surprising result was an improved team, giving Nystrom the confidence that the core group in Dallas is built to return to the postseason.
"It was amazing -- we got rid of Jagr and [Derek] Roy and [Brenden] Morrow, everybody thought we would collapse, but we got opportunities for a lot of young guys, and guys on the team played a little more and we had a hungry team that almost snuck in at the end," he said. "We have some good young guys. Jamie Benn is emerging as a talent, we're expecting a lot from him. Ray Whitney has been awesome for our team. And Kari Lehtonen between the pipes -- it's a team moving in the right direction, for sure."
Leading that direction is new general manager Jim Nill, who was hired April 29, one day after Joe Nieuwendyk was fired after four years on the job. Nill was part of the Detroit Red Wings front office for 19 years, and as the man in charge of the team's drafts for most of his tenure played a major role in the Red Wings' run of 22 straight seasons in the playoffs.
"He's really excited and he has a high pedigree coming from Detroit," Nystrom said of Nill. "He knows what it takes to win and the structure a team needs to be successful in this League. I think he's really keen on developing players. We've had some instances where we've had to rush guys and they're adapting to the NHL in the middle of the season rather than developing and making a significant impact. I think he likes a more veteran team. It'll be interesting to see what happens in the next little while."