He is just trying to pressure the Warriors to give him a max contract as he is part of the big 3, it's just unfortunate that his performance is not so impressive in the playoffs although they won the championship. However, in the end, it still depends on the decision of the Warriors if they will give him a max contract or not, and it's also up to Green if he will look for another team to give them what he is asking for.
If you had said Draymond Green was part of the big trio a few seasons ago, I would have certainly agreed with your statement. However, based on last season's results, Green's performance hasn't been impressive, and he's definitely not part of the big trio anymore. Maybe some will disagree with me, but it seems to me that Curry, Thompson, and Wiggins can be named as the Warriors' big trio at the moment.
Maybe his contributions is more on keeping the mentally of the players to be competitive. It's more of the intangibles for Green this season, he doesn't need to score more as there is Wiggins, but he bring the tempo, setting up the screens to free their shooters and then there is this defense of him. One thing I remember is when he stripped the ball from Jokic to seal the win for them in their series. That's Green contribution for them. So he is still part of the big 3 of the Warriors. Wiggins and Poole just make them very formidable as another set of offensive weapons, hence the 'death squad'.