The thing about matching an offer sheet for an unhappy player is a lose-lose situation for both the team that holds the player and the team offering. It's always more efficient just to bite the bullet and make a trade that works better for both sides.
If that is an accurate depiction of the situation, he will probably get traded before July 1st, for a more useful package than OS compensation.
Based on the current compensation, a team could go 5 years 9.16M and only owed a 1st, 2nd, and 3rd. It should be a bit higher next year, maybe close to 10M. Buffalo matches that and overpays Peterka, the team doesn't get the player and pays a huge opportunity cost by tying up 9M+ of cap for a week during free agency. Or if Buffalo doesn't match, the team probably could have gotten Peterka signed to 8 years at less than that cap with a sign-and-trade. Even if it costs them a bit more in assets, they get more value overall from a trade l.
If that's an inevitable thing that will happen, it doesn't help either team. It makes more sense to accept the outcome and work on a trade.
Buffalo needs to win now, so draft picks or overpaying Peterka doesn't help them. It would make more sense to find a hockey trade that they think makes them better now like they did with Cozens for Norris.