Starcraft and Warcraft 3 had what they called "custom maps" that people would play competitively online, with completely different styles of gameplay than the original game.
There were probably thousands of custom maps, but over time "genres" of map became more popular than others.
Dota is one such map, but it became so popular that in 2013 Valve released Dota2. Valve got involved because a few of their employees were fans of the original Dota mod and they wanted to build a modern sequel.
Dota, in terms of esports (aka Dota 2), is less than 10 years old.
Dota as a genre can draw it's LINEAGE back to the original mod from 2003, but that's about it.