English isn't his first language so sometimes you have to take into account what could be lost in translation. I haven't seen his comments personally but it's possible that his comments aren't meant to be a demand for ice time but a sincere expression to management and Oilers fans that he wants to be more involved and be a part of the solution moving forward in Edmonton. Being a guy that your team relies on does usually require more than 10 minutes of ice time each game.
I haven't seen much of Oilers games but based on what's happening and what the large majority of Oilers fans are saying, management's approach doesn't match with the actual situation on the team. If their treatment of Yak is part of the maturation process for him as a player, it would probably seem more justified if the coach and management supported the same treatment for all the players who aren't doing enough and aren't playing their best. Fans are pretty annoyed with Eberle yet he's not joining Yak in the press box as a healthy scratch. When you see a collective poor effort, players should be taking turns in the press box, not singling out one player. I don't mind that Yak went to his agent about this but neither should have made public comments to the media.