The term Empire of Mexico, should refer to the times in which Mexico was a self-governed monarchy. It tghen shouldn't be applied to the time Mexico was part of the Spanish Empire, but neither to the period that the novel Frankenstein make reference to. In this case, when the book mention the EMpire of mexico, it is actually referring to the "Mexica" or Aztec Empire. This was a great empire that ruled a huge part of what today is Central Mexico for about a century, before the arrival of the Spanish, which cause the fall of this empire in 1521.

On the text, Victor mentions this empire when he reflects as how and why he should take more time for himself instead of just focusing on his studies. On his reflections, he thought that if the the "rule" that if no one would had allowed that any pursuit interfered with the tranquility of domestic affections, many things in his tory would have been different, including that the empires of Mexico and Peru wouldn't have been destroyed.

At first I thought that the book was going to mention the actual, first Empire of Mexico (1821-1823), but after corroborating the dates, and then reading the text, I found out that it was actually referring to the Aztec Empire. I don't think that this former country was a huge intertest for the British of the time, but referring to this and to the Empire of Peru, may have had something to do with the fact that while Frankenstein was being written, the Spanish colonies in America (with some exceptions), were fighting for their independences at the time (a process that started around 1810 and lasted until part of the 1820's). This must have been a huge topic on Western Europe at that time, and considering their historical rivarly with Spain, as well as the fact that they lived a similar process some decades before, I think the process of Independence in Hispanic America awaken the interest of the British at the time.

Sources:

Memories and Notes from multiple classes and courses of Mexican History that I had when I lived there.

Picture from: Peel, Mike. (2015). Templo Mayor 2015 001. Recovered from: File:Templo Mayor 2015 001.jpg - Wikimedia Commons