Itch is self publishing game devs. Asking for admin rights is quite uncommon here. Who tells me, that the dev did not make a typo or copy pasted wrong instructions in released file and royally screws up my system with the escalated admin rights? Not even counting intentional malware from all those scam accounts with stolen game descriptions. Or a trusted account getting hacked and the hacker releasing "an update".
I suspect why unzip and run is preferred method of installtion and the classical installer method is just not seen, has other reaseons, but nowadays, asking for admin rights is a red flag. If it is missing system files, I can install those by other means. And when I understand you correctly, you could not even chose the destination.