If they are choosing to not stop to pee because they are playing a video game, there is a fairly easy fix. Get rid of the video games. If that is too extreme for you, set up a system where every so often your son has to stop and try to use the toilet before he can play again. Use a timer and go interrupt him and make him use the toilet. If you have to, turn off the game system. If he makes you go that far, no more video games that day. If he gets up when you say he has to, he can come back and play. Or set an amount of time that he can play video games. Make him use the toilet before he starts, and when he stops. Make it a short enough period of time that he shouldn't need to go if he went before he started. I would use some small reward if he doesn't argue about going to try to use the toilet. If he argues enough that you have to turn it off, then no more games.
You need to make him clean up his mess. If he pees on his laundry, he can learn to do laundry. If he pees on the carpet, that is what enzyme stain treatments are for. Also what carpet cleaners are for. If he gets an allowance, he can pay for some or all of the fee if you rent a carpet cleaner. You could also have him contribute to the cost of the cleaners. Make him at least help, if not do it all. Use a blacklight to see how well he has actually cleaned. Check it often with the blacklight (I think you can buy blacklight bulbs that will go in any lamp) and if it shows urine, make him do the cleaning. The more work, and the more inconvenient that cleaning is, the better. Keep an eye on it and insist he keep working until you are satisfied. Be aware that some cleaning products may also glow under the light. Test it before you evaluate the quality of his work.
