There's been a trend the last few years of depriving the GM of his power. In the past, the GM was always the guy at the top of the shot-calling pyramid (but for the occasional overly involved owner), but you're seeing more teams experiment with different executive hierarchies and structures. In places like Colorado, Toronto, and Calgary, for example, you don't see that omnipotent GM ruling unilaterally.
If the Coyotes name Chayka their GM, it's clear he wasn't their first choice. Their other pursuits may or may not have turned down the opportunity because they wouldn't have had as much power, and I imagine the resulting structure of the front office would be different depending on the experience and philosophy of whoever becomes general manager, but if Chayka is the guy, it's because the decision-making, negotiations, etc. will be spread out.
The fears about Tippett having a larger say in management are certainly founded, but my worry goes beyond that. I'm as skeptical about his talent evaluation and team-building approach as anyone, but if he has a more hands-on role in management, he'll be less focused on coaching. Whatever you think about his coaching ability, it's definitely going to suffer if he spreads his attention more thinly into other areas, and I don't really trust the rest of the staff to pick up the slack. Today, the Coyotes have one of the best coaches in the league. A move like this could negatively affect both their management and their coaching.
But maybe this is the Coyotes taking the long view after all. Maybe Chayka is just a patsy to hold down the fort until Tippett transitions completely into a GM role, letting Tip time develop Newell Brown into a head coach in the meantime.