The unit speech in Age of Empires seems like a made-up one, a kind of "Simlish" (warning TV Tropes). Is it completely made up, or was it somewhat based on a language? Some of the responses sound vaguely Latin, with the -us suffixes.
Unfortunately I cannot find any sources for the original Age of Empires, but every game in the series from Age of Empires II onwards (AoE III, AoM, etc.) have in-game dialogue based on the language of the civilization (with exception of the Atlanteans in Age of Mythology, who speak a made up language).
You can find the unit speeches and translation on the Age of Empires wiki - for example, here's the one for Britons in Age of Empires II.