Literally, this would mean seated on the window, but in English we say sitting. To use the continuous in Hindi - raha - implies a continuous action of a transition from standing to being seated. In other words, that very short time when we bend our legs and before we land on the chair!
Pigeons perch or sit on window sills all of the time. Apparently Hindi is a more expedient language in describing this.
Anyway, the real question I would like some sage pundit to enlighten me on is why, if Hindi is an SOV language (Subject-Object-Verb) is the Window first in this sentence. Isn't the Window the object and the Pigeon the subject?