I presume he has been assessed by a Speech and Language Therapist? Even if he has I would request one again and ask that his expressive and receptive language is assessed as well as assessing for Semantic Pragmatic Speech Disorder and Auditory Processing. This should help identify how much of what you say he understands.
You also need the SALT or Educational Psychologist to assess if he can identify emotions from either facial expressions, tone of voice or words being said. If he cannot identify your emotional state he won't react appropriately. Infact, as in cartoons, he may think it is funny.
Regarding the over reaction, that is typical but not acceptable. There are two difficulties here. One is that they find losing or not being able to achieve something very frustrating. Secondly they have a different neurological brain structure whereby they find it hard to control their feelings. So whereas we might get a bit annoyed, but keep that in check and get over it quickly, they cannot. He will get totally flooded with emotions that he cannot bring under control or get over easily. Hence the tantrums and anger.
Maybe he needs games that he can succeed at more. Or if that is not possible maybe he is too young for it, or maybe a different type of system. My son is 7 and I am now starting to think about a computer gaming system for him. He too would find losing difficult. He would also find it hard to look at the screen and manipulate the controls at the same time (ie. multi-tasking), so I am looking around for a system that is more autism friendly. At the moment he can only watch other children playing the games.
But social interaction and behaviour is the responsibility of the SALT and the EP and the nursery/school. They should be starting to teach him how to recognise his emotional state and how to calm himself down. They should be giving this advice to you as well. I would send a letter to them both. Speak with his nursery to see if he has the same outbursts there as well. If so the nursery should also be getting professionals in for advice.
It may be that he cannot cope with the computer games at his age. If so remove them. In circumstances where he is hitting or kicking you, tell him firmly that kicking/hitting is not acceptable behaviour. Then take him to his bedroom and tell him he needs to calm down. You can sit in the room with him, but don't speak or touch him as that can make them worse because they are overloaded from a sensory point of view and talking and touching is giving him more sensory information to process. When he has calmed down tell him that he cannot hit and kick you. At his age, and with language difficulties, you aren't going to get an explanation even if you ask him. But you can ask him questions like 'Did the computer game make you mad'. 'Did you lose and it made you angry'. Then you can give an explanation like 'When we get angry we need to calm down' 'We calm down by going to a quiet room'. Then you really need advice from SALT and EP.
I'd suggest to take away the computer and video games. If he can't behave with them, remove them from the house (store them at a relative or friends for awhile?). Or lock them up in a closet for awhile. Not sure how verbal he is, but you could talk to him when he is calm and explain why you took the things away for awhile. Maybe he is not emotionally mature enough to handle it? My daughter used to freak out when she plays this electronic toy (it's meant for 5 and 6 year olds and she's only 3) when she got an answer wrong (it's a quiz toy that has fill in the blank letters for words). I couldn't deal with her crying and having a meltdown over a stupid toy so I donated it to Goodwill and just got it out of the house and out of her life. Well, she doesn't have enough language to ask where it went but I think she forgot about it at this point since it's been several months.