I believe icehouse's space and proximity to residences plays a big part in why it works for Variety and not them. They have to have X% of revenue from food to have beer and entertainment in the same space. Hence the need for Atlanta to ease up on their licensing bs. Variety doesn't have to worry about it unless they make it up in popcorn sales. That's some expensive popcorn.
The relevant ordinances are an absolute pain in the ass to wade through (Sections 10-88 and 10-94 of the COA Code of ordinances - available
here), but the Icehouse and Variety enjoy the exact same exception to the standard distance requirements.
There is a restaurant exception to the distance requirements [10-88(e)], but that's not the one the Icehouse operates under. It avoids the distance requirements through the exception at 10-94(b)(2), which works by selling only beer and wine within a specifically described geographic area (basically the village). Hard liquor sales would prevent them from being able to apply this exception. The Variety (and possibly other venues in L5P) is exempt from distance requirements under the exact same exception, actually at 10-94(b)
(1), except the description of the geographic area is L5P.