11 year olds are perfectly capable of understanding that if someone is doing something they don't need to immediately stop to listen to them. If Op was drying her hair and he didn;t like it, he could have waited until she had finished - it wasn't an urgent matter that needed to be discussed.
Asking him to discuss it with his dad isn't dismissing him, it is offering a better solution, as it is involving the person who will be sharing the game with him, so paying for game needs to be negotiated between them not OP.
We do all our children a disservice if they think that they only have to scream and swear and someone will jump. In the real world we have to learn that sometimes other people may not be able to give us their full attention immediately and that we are not always the priority.
11 year olds should be well past the stage of screaming for immediate attention. And analysing his every feeling at every moment (based on pure speculation)and pandering to him is so cruel - not letting children learn to cope when things aren't exactly as they want them right now is so unkind as it doesn't let them learn how to deal with feelings of irritation and doesn't allow them to be independent and learn how to problem solve by themselves.
At 11 yrs the DS is well able to think 'I'll wait until Mum's finished drying her hair then I'll ask her about my game' or 'Actually it's probably best to ask Dad - he and I are the gamers and we'll be sharing the game. It's not really Mum's problem to sort out.'
Op - I would wait until he is calm, get him to clear up the mess he has made, make him contribute towards the cost of replacing any broken items of crockery etc., wipe the carpet where drink/food has been spilled.
Then maybe later today I would sit down with him and explain that this sort of behaviour cannot go on, screaming and swearing when you don;t get your own way is completely unacceptable. Then I would ask him how how thinks he could handle such situations differently, how he can think of ways to calm himself if he finds he is getting cross. And what he thinks the consequence should be if someone swears at another person and calls them names.
Then draw up a plan together of how things will go next time he finds himself losing the plot over nothing.
Teach him that he can master his negative behaviour he is clever enough and old enough, let him feel the sense of achievement that comes from behaving the right way and controlling your irritation and working out better solutions than losing your temper.