I recall seeing a system that consisted of two planar components (and I am fairly certain those were aromatic) that could couple to form the product. The self-catalysis consisted of a product molecule acting as a template for two component molecules to absorb to, which was claimed to have increased the reaction rate.
Edit: I have found the system I was thinking about. The Asker may decide for themselves if this fits the bill. The example is given in K. Ariga, T. Kunitake: "Supramolecular Chemistry - Fundamentals and Applications", Springer, 2006, p. 31. doi: 10.1007/b137036. As of this writing, the page in question is available through Google Books and the reference list for the section (2.10) is on the publisher's page. I was not able to definitively select the correct reference and I do not have access to them, anyway. Note that Ariga & Kunitake seem to have up their mind on what to call it:
In this system, [the product] acts as a template for self-replication. It may be surprising that a simple host-guest system like this mimics the fundamental activity associated with life, self-replication.