Let's travel back in time. All the way back to January 2013. Larry Elison, CEO of Oracle, had recently spent a bunch of money buying the island of Lanai and wanted to make sure visitors would still be able to get to the two Four Seasons hotels on the island. Island Air was in bad shape, with not a lot of money and Dash 8-100s that were running out of cycles and working on replacing them with worn out ex-American Eagle ATR 72s. While technically possible, jet service to the island had never been a fiscally sound thing to do (I remember Aloha advertising it at one point and Hawaiian ran a triangle route with load restricted DC-9s between Honolulu, Molokai, and Lanai) so Hawaiian 717s were unlikely to show up anytime soon. Mokulele's tiny 9-seat Cessna Caravans were likely the type of experience he wanted for the guests of his high end resorts.
So buying Island Air made some sense. The ATRs, while not a large jet, would at least provide the familiar experience of flying a regional airliner on the short interisland hop. Trying to position itself as the #2 airline probably didn't seem like a bad idea either after the failure of the much-loved Aloha and much-despised Go, a position in which Island Air pretty much was in whether they wanted it or not. A lower cost/lower fare turboprop alternative to the mainline jets had been tried before, but there was the potential to be more successful with just one big competitor (Hawaiian) rather than two (Aloha and Hawaiian). But Island Air was never seemingly able to shake the poor reputation they developed when they didn't have enough Dash 8s left to fly the schedule and once the ATRs arrived couldn't keep them flying either, resulting in delays and cancelled flights.
So Hawaiian smelled an opportunity. Go was gone, Island Air had a poor reputation, and Mokulele was too small to be relevant. They bought some ATR 42s from Europe, contracted Empire to fly them, and reentered the Molokai and Lanai markets they hadn't been able to viably serve since retiring the Dash 7. Almost immediately, freed from the obligation of providing the only regional airliner sized service to the island, Island Air dropped service to Molokai to focus on Ellison's Lanai. But with Island Air continuing to lose money and Hawaiian's ATRs not seemingly going anywhere and able to bring guests to the resorts, it makes sense for him to stop pouring money into the airline and let someone else figure out what to do with it.