No, there is no indication that the other ship was Tamarian.
The language used, "eyes in the dark" and "one moon circles", are telepathic messages as explained by Deanna Troi. There is no indication that the aliens in the other ship literally send these words. For all we know they telepathically send images of the binary star system, which Deanna "sees" as two eyes in the dark, and a schematic depiction of a hydrogen atom, which Deanna "sees" as a planetary system.
Since we do not know if words or images were telepathically sent, we have no way of knowing what the aliens' actual language is, or if they have a (spoken) language at all.