#C, 149 bytes, not tested

#include <stdio.h>
#include <unistd.h>
#include <stdlib.h>
int f(char *s){int n;while(*s){sleep(n=rand()%10+1);for(;*s&&n--;s++)printf("%.*s",1,s);}}

to run, add

int main(){f("Programming Puzzles & CodeGolf");}

then compile and execute

C, 149 bytes, not tested

#include <stdio.h>
#include <unistd.h>
#include <stdlib.h>
int f(char *s){int n;while(*s){sleep(n=rand()%10+1);for(;*s&&n--;s++)printf("%.*s",1,s);}}

to run, add

int main(){f("Programming Puzzles & CodeGolf");}

then compile and execute