90ish point and click adventure (in space?)
 

The thing I remember most was at one point you had to hide from something that was chasing you, and you hid in an arcade. In this arcade you could play Barnstorming.

At least 256 colors I think, I'm also pretty sure it was set in space. I think the protagonist was a blonde kid.

Could it be Space Quest 4? The arcade is one of the many locations you had to explore. :)

http://www.mobygames.com/game/space-...rs/screenshots

I think the game is the space adventure, I recognize the bit you are on about in the arcade :D


https://en.wikipedia.org/wiki/The_Sp...re_(video_game)

Just to add another idea, I think there was something about arcade in Future Wars - Time Travellers.