Team games are quite popular in StarCraft Brood War - not only 2 vs 2, but often 3 vs 3 or even 4 vs 4. In fact the 3v3 and 4v4 games were usually played by lower skilled players, due to the relatively lower skill cap and relatively random results (at low skills win or lose depends more who you get on your team than your own actions).

Brood War also has custom maps with relatively crude, but still use programming (loops and triggers) that allowed players to build thousands of various custom maps. MOBA genere and (probably) tower defense comes from StarCraft Brood War custom maps. There were many other categories (e.g. bound maps, puzzle maps, control maps) that are poorly represented even nowadays.