Yes and No. There is a lot of time spent in front of a computer but also just as much time set in loooooong meetings. And a lot of time with a good old fashioned pad and pen.
Do game designers need to use the computer to work?
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There's a lot of time spent WORKING on the computer. Playing games is often done on your own time, but you probably need to do this to stay on top of things.
Playing games for 3 hours a night (if that's all you're doing) isn't helping you learn to be a game designer because it's such a small part of the job.
When I was in high school I definitely played games 2 hours a night on average. I don't think I even get in 2 hours a month these days.
Except you can use maya/blender and unreal/unity on your phone then yes, you do need a computer because you have to program the game or model the assets.
I actually have written code in the drop box app a few times, not the easiest experience, but it works when you need to get something done quick!