Although Galen spent much of his career in 2nd century AD Rome, he was from the eastern part of the empire, which always remained primarily Greek speaking, and wrote in Greek. In fact, most “scholarly” writings from throughout the Roman period were in Greek, and, in fact, the Byzantine Empire, which succeeded the Roman (and, in fact, continued to think of itself as The Roman Empire through its many centuries of existence, despite having its capital in Constantinople, not Rome) was Greek speaking.
Like you, I am a bit surprised to hear that much of Galen’s work remains untranslated, but then again, he did write a fuck of a lot, and by no means all of it was about medicine, where he had some idea what he was talking about. He wrote extensively on philosophy and other subjects. I do not think he is generally reckoned to have been a very good philosopher. Even so, though, his philosophical works are probably of interest to historians of philosophy because they probably contain information about the views of more important philosophers whose own works do not survive.
I think it worth noting that the stuff that roger_pearse seems to be talking about is Greek from the Roman Empire period, plus, perhaps, from the Hellenistic era that preceded it and the Byzantine era that followed it. (Indeed, being more recent, there is probably much more that survives from the Byzantine era.) I think that there is little or nothing that survives untranslated from the earlier era of Classical Greece (the era of Plato, Aristotle, Sophocles, Euripides, Herodotus, etc.), let alone the pre-classical era that preceded that. For instance, despite their huge historical importance, none of the writings of the presocratic philosophers from the pre-classical and early classical era have survived, except for short fragments - generally brief quotations or paraphrases found in the works of much later (mostly Roman Empire era) writers. Likewise, the works of famous and influential pre-classical era poets, such as Sappho, survive only as fragments. (Despite its fragmentary nature, however, this stuff, both philosophical and poetic, has been translated, and is generally readily available in English.) I think when most people (probably including the OP) ask about “Ancient Greek texts” they are thinking of ones from classical or pre-classical Greece, not from second century Rome (like Galen) or 8th century Byzantium, and probably not even ones from Hellenistic Egypt or Pergamon.