[There is no "drunk in public" law in Anchorage.]
There are and there aren't depending on what Arthur meant.  Alaska takes a more humane approach to public drunkness.  For example, AS04.16.040 makes it illegal for a drunk to enter a venue that serves alcohol and AS47.37.170 provides for a police officer or emergency service provider to take into custody (arrest) a drunk in public.  However, these are to protect the drunk from harming (or further harming) him or herself.  It really doesn't serve as an deterrent to being drunk in public as Arthur appears to present.