I've seen First Air's 737s in my various travels. Much like Inuit Air's, they're the old models with torpedo engines on them.
I suspect a lot of these flights are heavily subsidized.
In addition to being cheap to buy, the -200 models have the best short-field performance and are less susceptible to picking up foreign objects on less maintained strips. In the past, they were flown into Unalaska/Dutch Harbor with its 3900ft runway.
Wow. That's truly the frontier. "There are two nurses at the medical station....."