No it is not anywhere necessary to have a good drawing skill in case if you go for game designing. Most of the graphics development are now done on computer so you will be working on it only. But it is an added advantage if you that skill.

Hello Hardik,

No, not necessarily. Nowadays a lot of game designing is done thru software, so it would help more if you knew animation and coding. An aesthetic sense will always help, though.

Moreover, there are other functions in game design apart from set design. You could create storyboard/music too, requiring no painting skills.