Why I do not see document type for Purchase Order in Cloud Integration gateway (CIG) Mapping Tool ?

You need to check if you have at least one project created and deployed to In Testing status for that Product:

1. Log in to CIG.
2. Click My Configuration > Projects.
3. Click Create a New Integration Project, for example, for procurement.
4. In the Project Wizard Add New Connections and Click Next till you confirm and deploy the project in test environment.
5. Once Deployed the Project will be In Testing Status.
6. Now Click My Configuration > Mappings.
7. You should be able to see documents related to the project you created, in this example, procurement related document types.

SAP Ariba Buying and Invoicing
SAP Ariba Buying