"Rat Dota" is a term used in the very popular MOBA game called Dota 2. It means that one of the teams (Radiant or Dire) are pushing one or all three lanes and damaging turrets and/or structures but not committing to team fights.
Basically referring to a rat. Chipping and gnawing away at an object and then running away at the first sign of danger.
Natures Prophet TP's into a pushed lane when the enemy team is on the other side of the map and deploys his treants. Someone else on his team uses Boots of Travel and teleports onto natures treants. They both push that lane and do a large amount of damage to enemy structures very quickly. The enemy teams teleports back to stop the push, by the time they get there the damage has been done and the two pushing are long gone and doing the same to another lane.
Rat Dota at its finest, and very annoying.