Does children under a certain age have rights to play violent video games

of course they do. but of course with parental permission & guidance given with them. threat games like movies. they also have a ratings system. in America it is called the ESRB. here is a breakdown of the system for you

ESRB rating movie rating
Ec - E G
E10+ - T PG
some T - M PG-13
A NC-17 (X)