"Limited video lottery retailer" means a person who holds either a valid license issued under article 60-7-1, et seq., of this code, to operate a private club, or who holds a valid Class A license issued under article 11-16-1, et seq., of this code, to operate a business where nonintoxicating beer is sold for consumption on the premises, or who holds both licenses, and the person also holds a valid limited video lottery retailer's license issued under this article.