Issue
Approve on behalf using the admin role user is possible.
The system will prompt an approver authentication window when approved records from the admin role.
Cause
The "Approvals with e-Signature" plugin is activated on the instance, so you see this behavior.
https://<instance-name>.service-now.com/v_plugin.do?sys_id=com.glide.e_signature_approvals
The behavior is as expected because of the activation of "Approvals with e-Signature" on the instance.
Resolution
In case if you don't want the Approver Authentication to be shown when approving on help, then there is a way to De-activate e-signatures.
Set Enabled to False on any tables where e-signatures are no longer required, from the below list:-
https://<instsance-name>.service-now.com/e_signature_registry_list.do
This will disable the functionality of showing Approver Authentication popup when approving a record by a different user.
Related Links
Reference documents:-
https://docs.servicenow.com/csh?topicname=r_ApprovalWithESignature.html&version=latest
https://docs.servicenow.com/bundle/newyork-servicenow-platform/page/administer/service-administration/reference/r_DeactivateESignatures.html