There are a lot of very old written histories recording various battles. For example, the Spring and Autumn Annals have a somewhat detailed account of the Battle of Chengpu and its aftermath: https://ctext.org/chun-qiu-zuo-zhuan/xi-gong#comm18160 This map actually briefly flashes a red dot at 632 BC, but since it's not part of any named war, you could easily miss it.

The areas where you see fewer wars don't necessarily lack written historical records, it might just be that nobody bothered to translate those records into a machine-readable format yet. (I'd guess this map is based on Wikidata.)