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. 

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.

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. 

Reference documents:- 

https://docs.servicenow.com/bundle/newyork-servicenow-platform-capabilities/page/administer/service-administration/reference/r_ApprovalWithESignature.html

https://docs.servicenow.com/bundle/newyork-servicenow-platform/page/administer/service-administration/reference/r_DeactivateESignatures.html