I do understand what it's like to have a teen who isn't happy and isn't talking to you. It's positive that both of them are open to counselling (ours never went although we would have loved him to) as it means they have an outlet.
You say he 'games all day'. This is not good, particularly when there is depression. I know every case is different, but in case it helps, we took away the computer (by removing the cable) which was greeted with some shouting and crying but followed quite rapidly and quite incredibly by a huge improvement in his mood and an interest in real food.
We also dealt with nocturnal living and school refusing. All this, in our case, came right when we took away the computer and gave it back only as a reward for good behaviour, attendance, work, etc. He was 13 when we did this, and I do appreciate that your 17 year old will need a different approach.
I tried to use really positive words and compliments (even when feeling murderous) and also tried to use time in the car, when you don't have to look each other in the eye, to have conversations. I used the technique in how to talk to teenagers so they listen and listen so they talk. It's not complicated, just give non-committal answers, judgement free answer to their comments.
We also offered to pay for anything he wanted to do outside of the house.
Have you thought about having some counselling? I did and found it very useful to talk things through.
How are they doing at school now?