@Mterwoord If you are pinging in code using TIdIcmpClient, then YES, you need admin rights, as TIdIcmpClient uses a RAW socket, not any OS-provided ping APIs. RAW sockets are restricted to admins on most platforms, including Windows:
https://support.microsoft.com/en-us/help/195445/: "A Socket or WSASocket call that specifies the SOCK_RAW socket type fails with the following Winsock error message (10013 WSAEACCES) if the user is a non-administrator"