Loan is for the purpose of constructing a multifamily property. It is set up as a construction to permanent situation. Interest only payments for one year and then fixed for the rest of the term.
It is secured by a second mortgage on a different multifamily. What would be the purpose of this loan?

The purpose of the loan is construction - so purchase for HMDA.

Agree.

What if the borrowers already owned the land that the cabin is being built upon?

Owning the land prior to the construction loan is not a factor. HMDA is all about dwellings, not land. The construction of the dwelling is the "purchase" for HMDA, assuming it's not temporary financing. Think of it as purchasing the materials needed to construct the dwelling.