Hi Gerard,
Yes, "local integration engine" refers to the engine in the ECC ABAP stack. When using Enterprise Services with PI, you have the option of using either the XI3.0 proxy protocol (which uses the local integration engine) or SOAP (which uses the Web Service runtime in ECC ABAP stack).
If your non-SAP ESB has capability to transmit over SOAP, it should be fine. The ESB just needs to consume the WSDL definition of the interface (can be retrieved via SOAMANAGER) and generate the SOAP message accordingly.
What I meant by "SAP-delivered Enterprise Services" are those interfaces that are developed by SAP and delivered as standard content on the ECC/SRM/CRM/etc system. It is also possible to develop custom interfaces (but maybe this might not be called Enterprise Services)
You can look through the Enterprise Services Workplace at the link below to explore more about what is readily available by SAP.
Rgds
Eng Swee