The players don't care about the Kings. If they play in a playoff game, and happen to score a game winner, that might mean $500k more in their next contract. If any of them happen to have a John Druce run in the playoffs for some random ass reason, that's probably a 5 year contract worth tens of millions of dollars.
Your first sentence doesn't matter. Fans care about that. Players don't. All they want is another game to try and win. They don't care about draft picks. They don't care about the franchise in 4 years. They live for today. Doughty doesn't care about the franchise, he just wanted to play in an important game again. Oddly enough, he won't one way or another this year. Mike Richards didn't care about the franchise when he didn't willingly walk away when he clearly couldn't play anymore. Justin Williams had the audacity to care more about his wife's opinion than this franchise when he moved back east. He could've signed here cheap, but no, he had his own agenda. Carter didn't care about the Kings. If the Flames and Kings play in a series, Sutter isn't going to think, you know, that's the franchise I won with, I hope they beat us. No. He hopes Byfield plays, and hopes to embarrass him, just so he can have one of his clever Sutter quotes.
I don't know why you're on this Grundstrom kick. He's not a UFA. He's not a high profile RFA.