Thanks for the replies.
41N, yes, it does resemble Oriental Breeze, but OB doesn't have the purplish new leaves that this garden variety does. It also resembles Cardinal, though that one looks lighter green. Neither one mentions the licorice flavor.
Filmnet, yes, it tastes more like a Thai basil, but the inflorescences are very different.
I'm guessing there are a bunch of other ornamental basils around. Maybe the plant breeders were inspired by the wild variety in ornamental oreganos and decided to do some work on basil.
Now I wish I'd tried to root the stem my neighbor gave me and overwinter the plant!
Added: It resembles Langkuri or Siam Queen, but seems to have a fluffier inflorescence than either one of those.
http://www.kitazawaseed.com/seeds_thai_sweet_basil.html