These games used the GoldSrc engine. Any game built on this engine gets called a mod. But this is not what most people actually think of when people are talking about mods. Rust is not a mod of Unity. These are game engines that people built a game using.
>DotA
This was a custom map. Not a mod.
>LoL, HoN
These were built on in house game engines and were not a mod.
Counter-strike was definitively a mod, you had to install it in the same folder as Half-Life and start it with 'hl.exe -game cstrike'. It became a standalone game later with the retail release.
Calling DotA just a custom map is a bit of a stretch. That was merely the packaging. These "custom maps" had various scripting capabilities that made them more than just some terrain.
Also custom maps are mods by definitions anyways, with the exception of games where the creation of maps is a component of gameplay.
I mean, to those who played them, 'custom map' is basically just a term of art indicating the things you said. In the parlance of the mid-2000s WC3 scene, you would call them custom games or custom maps.
Or, if you were slightly older, you might call them UMS, as they were in Starcraft. Short for "Use Map Settings", indicating that the game logic should come from the scripts and triggers in the map file rather than the built-in logic for ladder games.
Every MOBA that exists (DotA, LoL, HoN, etc)
Team Fortress
Killing Floor
PUBG
Natural Selection
Undoubtedly, many more that I can't recall off the top of my head.