If you want a non-admin user to be able to remotely reboot servers (with shutdown -m command), but don’t have other admin rights, you can achieve this with a single group policy change.

If you want this to apply to a single server you can user local group policy, for multiple servers, use global domain group policy.

The policy you need to change is located in:
Computer Configuration > Policies > Windows Settings > Security Settings > Local Policies > User Right Assignment > Force shutdown from a remote system

Simply add account(s) in question to this policy and they will be able to reboot servers remotely.

Example reboot .bat file:
shutdown -m \\192.168.5.6 -r -f -t 0
pause