Because there's no evidence linking happiness and enjoyment to successful healing. Nope. None at all. And Hosptials are happy wonderful places where children can feel completely comfortable and relaxed as they heal from whatever ailments are requiring their prolonged stay. Yep.
Just sayin', those "just Video Games" can help the children feel more comfortable and relaxed. It's something familiar to latch onto in an alien environment. And if you're recovering from say a potentially life threatening surgery, that can make a difference.
Just because the rest of the world has troubles doesn't mean you should stop making your little corner of it better.
Heck, I remember I once had surgery as a kid. Wasn't life threatening, but some teeth grew in the roof of my mouth somehow (beneath the skin layer) and had to be cut out. Which meant the roof of my mouth needed cutting open. Which meant surgery. I swallowed a lot of blood during the surgery whilst unconscious, had some trouble coming out of the anaesthetic and threw up the blood I swallowed every time I tried to stand. So they kept me overnight at the hospital.
An alien environment, nobody I knew there, people coming and going constantly, lots of noises. I remember it being rather unnerving and kinda scary. I also remember getting to play Sonic the Hedgehog on one of the old Sega Mega Drives they had in the children's ward, which made me feel better xD Don't underestimate the power of something familiar in a strange and alien environment, especially for a child.