The legislative materials to the State Treaty now explicitly state that esports can be considered sports. However, the responsible authority must examine this on a case-by-case basis. This authority (Regierungspräsidium of the city of Darmstadt) has so far refused to do so. Details can be found in following publication (in German):
Zulässigkeit von Wetten auf eSport-Ereignisse nach deutschem Glücksspielrecht (Admissibility of Bets on Esports Events Under German Gambling Law)
In addition, the new law on the taxation of betting on esports (§ 15 RennwLottDV) came into force on July 1, 2021. Details can be found in following publication (in German): eSport im Fadenkreuz der Sportwettensteuer – Eine Analyse des § 15 RennwLottDV-E (Esports in the Crosshairs of Sports Betting Tax Regulation - An Analysis of § 15 RennwLottDV-E)