How are self-replicating modules essential to the most popular hypothesis about the origin of life?

I have not heard the term "self-replicating modules" used in the context of the origin of life, OoL, but conclude it is intended to describe ostensibly the simplest initial organism (s) that biology might consider to be the first life, even the last universal common ancestor, LUCA.

Reality is, there is no replication possible without DNA, the only organic compound that contains the required biochemical elements required to enable replication. RNA is insufficient to self-replicate. Actually, DNA itself does not self-replicate, but is essential in the process. Consequently, only a fully assembled organism will self-replicate, meaning a multitude of proteins, enzymes, ribosomes, RNA and key supplies of required elements and molecules are necessary to allow self-replication, all of which must be brought within a cell structure, filtered from pollution and contamination.

To answer the question, the first, self-replicating elements of life are intelligently designed, irreducibly complex biochemical assemblies that are functionally sufficient to reproduce. DNA is the key for this and there is no evidence that anything simpler can accomplish self-replication.

Regarding the "most popular hypothesis," the present field of OoL research is a chaotic mess with no explanation of how the first life started. There are no naturalistic processes capable of producing the key elements required for OoL. The greatest unexplained issue is how did DNA get created. DNA is not part of the popular story because it is known to be too complex and known to be beyond any naturalistic process for formation.

Much else could be said about this, but the answer to the question is the modules are only relevant if defined as a complete functioning cellular entity.