As starting a ppp link implies configuring a kernel device (a network interface) and manipulating the kernel routing tables, special privileges are required - in fact full root privileges.
Fortunately, pppd has been designed to be 'safe' to run set uid to root. So you will need to...
chmod u+s /usr/sbin/pppd
When you list the file, it should then appear as...
-rwsr-xr-x 1 root root 74224 Apr 28 07:17 /usr/sbin/pppd
If you do not do this, users will be unable to set up their ppp link.