Depending on the OS, ping is either set setuid[1] as root, or more commonly these days, ping is granted a "capability"[2], such as CAP_NET_RAW on Linux. macOS does things a little different[3].
This allows non-root users to run stuff like ping without granting them full root access. You do not need to, nor should you, run the script as root.
% ls -l /usr/bin/ping
-rwxr-xr-x 1 root root 89768 Apr 8 09:00 /usr/bin/ping
% getcap /usr/bin/ping
/usr/bin/ping cap_net_raw=ep
~
% whoami
jake
~
% id
uid=1000(jake) gid=1000(jake) groups=1000(jake),4(adm),24(cdrom)
% ping -c 3 8.8.8.8
PING 8.8.8.8 (8.8.8.8): 56 data bytes
64 bytes from 8.8.8.8: icmp_seq=0 ttl=117 time=9.195 ms
64 bytes from 8.8.8.8: icmp_seq=1 ttl=117 time=8.837 ms
64 bytes from 8.8.8.8: icmp_seq=2 ttl=117 time=10.998 ms
--- 8.8.8.8 ping statistics ---
3 packets transmitted, 3 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 8.837/9.677/10.998/0.946 ms
Hope that helps. Happy to elaborate on any unclear points.1. https://unix.stackexchange.com/questions/382771/why-does-pin...
2. https://unix.stackexchange.com/questions/592911/how-does-pin...
3. https://apple.stackexchange.com/questions/312857/how-does-ma...
Edit: updated explanation a bit.