Part of 703-300:
“Dwelling” means any building or structure, though movable or temporary, or a portion thereof, which is for the time being a home or place of lodging.
Underlined the might be gray area of your back yard.
Residence
Dwelling
Domicile
Lodging
These words are often used as synonyms, but legally they are not often interchangeable.
Dwelling is defined as a building or structure. That dwelling may or may not be your residence. In context of the firearm laws, your current dwelling may be a place of sojourn -- a hotel room -- lodging. The addition of the words "Home" and "Lodging" in your quoted text further make the point that your dwelling is not necessarily your home/house, but it still must be a building or structure.
Hence, the definition of "building or structure" is all that needs to be interpreted. You can drink inside your dwelling, but you can't take the gun outside of your dwelling while intoxicated.
Once outside, it's a matter of interpreting the "places to keep" definitions as to the legality of having the gun sober, which is kind of off topic. If they wanted to make your entire place of residence off limits for intoxication and having a loaded gun, why use "dwelling?" "Residence" is already in HRS-134 multiple times.
I think they chose dwelling intentionally. They know you can drink inside your home and have guns in your possession. Can't prevent that. But they can try to prevent you from being intoxicated outside with a loaded gun where more people would be potentially at risk.
I don't see any gray area there. Of course, the Cops that respond to a complaint will have to know the law.