Do I need my own social concept as an operator if the venue already has one?

Yes. The duties apply to both sides, but they follow from different rules: as an operator you need the social concept under § 33c (2) no. 3 GewO for your own business, covering the whole company and its staff. The venue must implement player protection on site under § 6 in conjunction with § 2 (4) GlüStV 2021. The simplest solution is one shared digital system in which both keep their records.