"medicated products" came up in a Translators FB discussion. Works quite well.

@@ -12,0 +13 @@
+<gloss>medicated products</gloss>

Better as an "expl" gloss, paraphrasing a little.

@@ -12 +12 @@
-<gloss>quasi-drug (product that has a relatively mild medicinal effect and can be sold in general stores as well as pharmacies)</gloss>
+<gloss>quasi-drug</gloss>
@@ -13,0 +14 @@
+<gloss g_type="expl">product with relatively mild medicinal effect, sold in general stores as well as pharmacies</gloss>

That's a good point. Many people would have only a vague idea of what 'quasi-drug" is supposed to mean, and that makes my proposed definition limited in its usefulness.
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About your definition:
I don't think it's right to refer to "medicated ingredients". You can refer to a medicated *product* (e.g. medicated shampoo), but I think the *ingredients* of the product are "medicinal" rather than "medicated".
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After reading the following article, I have come up with another proposal:
"quasi-drug (product that has a relatively mild medicinal effect and can be sold in general stores as well as pharmacies)"
http://www.medicalnewstoday.com/releases/11926.php

@@ -12 +12 @@
-<gloss>quasi-drug (e.g. cosmetics with medicated ingredients)</gloss>
+<gloss>quasi-drug (product that has a relatively mild medicinal effect and can be sold in general stores as well as pharmacies)</gloss>

http://www.linkedin.com/groups/Dont-know-if-anyone-else-4133931.S.77023006

It's very Japanese to call things "quasi-.....", in fact when I Googled for "quasi-drug" the first 10 sites were either Japanese or referred to Japan. (I'm reminded of "Quasi National Park",) A sort-of waseieigo. As that site I quoted points out, it's a variety of product rather unique to Japan.

@@ -12 +12 @@
-<gloss>quasi-drug</gloss>
+<gloss>quasi-drug (e.g. cosmetics with medicated ingredients)</gloss>