If the plan document has language in it referring to the "act" and the act is identified in the plan's definitions as ERISA, is the plan, by default, an ERISA plan?

This looks like a pre-approved Corbel volume submitter document without any changes to pre-approved language.

The plan either is or is not an ERISA plan. If it is a non-electing church plan exempt from ERISA, it is exempt from ERISA no matter what words are used in the document. Conversely, if the plan is subject to ERISA, it is subject to ERISA no matter what words are used in the document.

However, if the plan is not subject to ERISA, the language of the plan will nonetheless control the rights of the participants by contract. So, for example, if the plan provides for the full set of J&S requirements, and if the plan provides for claims procedures in accordance with Section 503 of ERISA, etc., those plan provisions will form part of the contract with participants.