Can a kid make a video game

Sure! You probably can't make anything fancy without experience so start here.

http://info.scratch.mit.edu/Scratch_1.4_Download

This is Scratch, Lots of people know about it. You can't really make a full on Super Mario Quality game, but you can surely give game making a try.

Making a full RPG or Adventure game is a lot less easy cause you actually have to write code and all that stuff.