"They just don't care"
The tablet is where this belief lives. You said it was time. He said OK. He carried on. He heard you and chose the game, and that's not memory, that's not caring.
Adele Diamond, in a 2013 review that's the standard reference on the subject, set out what researchers call the executive functions. There are three at the core. Working memory, which is chapter 3. Cognitive flexibility, which is switching between tasks and seeing things from different angles. And inhibition, which she divides into two parts, resisting temptations and impulses, and controlling interference so that you can attend to one thing and not another. She traces how each develops, and the developmental progression runs through childhood and adolescence, and she notes that stress, lack of sleep, loneliness and lack of exercise each impair them, which is worth holding onto for half past seven.
Look at what coming off the tablet requires. A child absorbed in a game is attending to it, hard, and your voice arrives as interference. To act on your voice he has to notice it over the game, which is interference control, and then stop an activity that's rewarding him every few seconds in favour of one that isn't, which is response inhibition, and then hold "get ready for bed" in mind across the walk upstairs, which is working memory. All three of Diamond's core functions, in sequence, at the end of a day, in a nine-year-old who's tired.
"OK" and then carrying on isn't a lie. It's the first step working and the second failing. He heard you. He agreed. Then the game did what games do and the inhibition that was meant to carry him off it wasn't strong enough yet, and the "OK" was as sincere as it was useless. If you've ever said "I'll just finish this email" and looked up forty minutes later, you've done the adult version, with an adult's inhibition, and you don't think you didn't care about dinner.
Not caring would look different. It would look like a child who was indifferent to your reaction, and Sam isn't, or you wouldn't have a child who says "OK". A child who says OK cares about the asking and can't yet do the stopping, and the word for that isn't doesn't care. It's nine.
The practical answer is in chapter 19, and it's an arrangement that does some of the inhibition for him. A warning at ten minutes, a timer he can see, the tablet handed over rather than put down. None of that is giving in. It's recognising which of Diamond's three functions is being asked for and lending him the part he hasn't grown.