The Islanders played at Nassau Coliseum which is in the middle of LI since their inception. They moved to Brooklyn a few years ago and it hasn't worked out...so much so that the Brooklyn arena wants the Islanders out. New Islanders owners are trying to get an arena built roughly between Nassau Coliseum and Brooklyn. Meanwhile the Coliseum was renovated making it a bit smaller and not fit for NHL standards, it was small to begin with. But the Brooklyn arena and the Coliseum are run/owned by the same company and a deal was struck with the NHL to allow the Isles to play around half their games this year at the Coliseum.
As you noticed, the atmosphere has been nuts. Regular season games were similar. I think it's due to the Islanders coming back to their LI fan base, a smaller arena and the fans know this will be a short-lived return to where we had the Stanley Cup run and oh yeah the team had their best season since forever after losing their franchise player.
When the Islanders made the playoffs the powers that be decided the first round home games would be at the Coliseum and after that at Brooklyn.
If the Isles make it past the Pens look for the f****ng car where people are sitting in every other NHL arena.