It is a subject particle. 은 after a consonant and 는 after a vowel. There is also the 이/가 pair, which has basically the same role but is used when one wants to emphasize on the subject or when the subject of the sentence is a new information.
Besides the whole "over there" thing, proximity is also a factor. So I would assume whatever "that" the speaker is referencing is perhaps across the room, or the speaker and whoever he/she is speaking to is in a car and the dog is not.