There is listed just one "battle" in the Americas for all of time through 1500, the Tikal-Calamakul wars. This is a poor representation even of the wars we know occurred, let alone all the stuff we don't know happened due to the lack of writing systems.
This data set appears to not be a particularly well-curated dataset, and it looks to my (non-expert) eyes to have an intrinsically high bias towards high detail of some key Western European conflicts even beyond the general bias imparted by the fact that histories of Europe tend to be the most well-curated and accessible if you're an English speaker.
I agree. Here's a list of battles which took place in New Mexico (where I used to live) - https://en.wikipedia.org/wiki/List_of_battles_fought_in_New_... . The 1540 Battle of Hawikku, which is in the time period you mentioned, is missing, as are the other NM battles until the mid-1800s.
This data set appears to not be a particularly well-curated dataset, and it looks to my (non-expert) eyes to have an intrinsically high bias towards high detail of some key Western European conflicts even beyond the general bias imparted by the fact that histories of Europe tend to be the most well-curated and accessible if you're an English speaker.