I'm so sorry, Itsjusttoohard, this is a difficult situation for all of you to manage.
What I would recommend in your specific situation, is to ask the hospital if they have a counselling service that you can access. Or if there is a charity for the particular illness in question, because many of these charities either have helplines or can put you in touch with other families going through what you're going through. Although counselling or peer support doesn't always work, when either does or both of them do, this can be invaluable for all the family.
We've recently had a cancer diagnosis (most likely terminal) in the family and hadn't planned to tell our boys just yet, but the middle one (18) overheard us. He was inconsolable, cried his eyes out, I answered all his questions, we talked about death and dying and I told him that if he had any more questions or worries, to come to us. Told his older (22) and younger (14) brother the next day. Zero reaction. Even though I expected them all to react and process this differently, I was still taken aback. I hadn't expected a non-reaction. Like yours, both went straight to the computer and played games.
It's been about four weeks and we've since been able to talk more which has made clear that they are, all three of them, very sad and worried about what lies ahead. But they are also young, much of the severity of the illness and the strain of treatment is either unknown to them or purely theoretical knowledge gleaned from the internet. They're not imagining all the things that can go wrong, like we are. They're not worrying about how Covid is making this all so much more complicated, like we are. They're not fretting about how to manage pain when painkillers don't work anymore, like we are. They're not remembering all the other people we know with a similar diagnosis and how they died, like we are. I honestly envy them for that.
Also, it's quite normal and healthy for teens to engage in what they enjoy, including to get lost in computer games when they have worries. (That's also why I play computer games myself - to focus on the game and nothing else. It lowers my stress levels and it's nice to do something fun. Even when you have huge worries in your life.)
The one thing I keep telling myself is that even if they don't show they are affected, I know they are. So we made sure to let them know that they can always talk to us. And we keep all news very matter of fact, answer any questions they may have and find opportunities for them to open up. We are also open about our own feelings, because pretending we're fine would have made it harder for them to show that they are not fine. And on any given day, if we feel they would benefit from talking about it, and then we create the opportunity to do so, but they don't take it, we don't stress about it, because there will be others.
I hope you will find the support you need, not just for your boys, but for you as well. 