Privacy issues aside (it’ll only take so long for any pile of PII to leak), this looks like an effective and quick to implement make-shift solution (smartphones are widespread enough and venue employees can enforce the scan), though I’m not sure of how much benefit these QR codes are in Korea.
In Seoul—among highest in the country in terms of new infection cases—coffeeshops, study cafes and restaurants are routinely really crowded. I have been working or eating out in one of such places here every day past two months, and I have never have been asked to scan a QR code or noticed one. I’ve only learned about it thanks to your comment.
(That said, I haven’t gone to karaoke, clubs or jjimjilbangs, and I can’t speak Korean well.)
I think restaurants and cafes are a highly underestimated vector of SARS-CoV-2 transmission in Korea especially, since many of the customers aren’t wearing masks (because they’re eating) and often speak quite loudly (perhaps to drown out the inescapable loud music or from being drunk on a semi-mandatory after-work party). Usually bothersome just to me, now it’s objectively problematic—as some doctor pointed out in an interview about a choir group infection, literally the louder you are the more of your potentially-infected saliva is flying around.