I don’t want to be a Well Actually guy about it, but the original Genie absolutely is anthropomorphic. The very definition of it in fact. He is a non-human entity with human-like attributes.
My problem with the live action Genie isn’t that it looks like Will Smith, it’s that it looks so poorly done. They shoddily pasted his face onto an uncanny valley CGI body and the result is creepy and off putting. There are mocking photoshops of Tobias from Arrested Development as the Genie which actually look better than the real thing.
I do agree however that Genie is an extremely hard character to do in live action. All his reality bending capers will just look kind of off at best, or plain horrifying at worst.
I can see similar problems with many other Disney characters too. Imagine Sebastian from the Little Mermaid. A human face is pure nightmare fuel, so do they just make him a singing photorealistic crab or what?
Personally I have no intention of seeing this or any other live action adaptions except possibly the Lion King. I hope it bombs so Disney will reconsider its new obsession with remakes.