The reason for the continued existence of the term "roe deer" alongside the simpler term "roe" is probably that it's much clearer, given that "roe" is a monosyllable with other meanings (and also sounds identical to the word "row" in some of its meanings), and given that most people don't discuss deer that often.
Indeed, if you go back to the time when people did frequently discuss deer, you find that they even had different monosyllabic words for different kinds of deer: notably hart and hind for (male and female) red deer, versus buck and doe for (male and female) fallow and roe deer — not to mention fawn, stag, staggart, brocket (red), pricket and sorel (fallow), and so on. There's a neat little table on this page.
Relatedly, the word deer started out meaning simply "any kind of animal"; Online Etymological Dictionary says: "The sense specialization to a specific animal began in Old English (the usual Old English word for what we now call a deer was heorot; see hart), was common by 15c., and is now complete." (I have to keep reminding myself that deer is not a cognate of Latin -therium, though; different PIE root.)
On roe itself, Online Etymological Dictionary says: "Old English ra, from raha, from Proto-Germanic *raikhaz, of uncertain origin; perhaps from PIE root *rei- "streaked, spotted, striped in various colors."
The other species being "red deer" and "fallow deer," it does seem like "roe deer" refers to coloration. ("Red" and "fallow" both refer explicitly to coloration.)
Also relevant: the archaic use of the male form to refer to any group. So when Deut. 14:5 talks about "the hart, and the roe-buck, and the fallow deer," or when 1 Kings 4:23 says Solomon had "an hundred sheep, beside harts, and roe-bucks, and fallow-deer," it doesn't mean that he had only male red deer and roe deer; "obviously" what applies to harts applies equally to hinds. But it does mean that frequently we'd say "roe-buck" or "roe-bucks" in places where it might be ambiguous, rather than "roe deer," leaving "roe" only for places where the context is unambiguous and/or we're talking specifically about female roes (e.g. the Song of Solomon).