Sporting president is making one mistake, which is going back on his word, otherwise asking for a lot of money isn't really wrong at all. If he just came out and said "hey , I want 100 million, that's it" and that was the last of it, then anyone who paid 100 million would get him, that is even more than right now, and nobody could say anything, Gyokeres is a player under contract and the team decides how much they want, end of story.
Sporting president want to see how much those teams who're interested with Gyokeres willing to spend, that's why they keep increasing the fees until the specific time, most likely before August 15, it's when Premier League will starts.
I'm sure at the end of the day, Arsenal will sign Gyokeres during the current transfer windows.
Their is a saying in my country that says; a decision made in anger is always very costly.
If Napoli gets more angry that they can't force victor osimhen to go to Saudi Arabia and they decide that he wouldn't be going anywhere else, they are the one that it's going to affect the most more than the player, because during his final season that he is not playing, they must pay him every penny, and they are definitely going to lose him for free, which is going to be a big blow to the finances of the club.
Napoli want to make money because they need to cover their losses from signing and salaries for Conte, De Bruyne, Lukaku and likely other new players they want to sign next.