1) 0 - Character Advancement:
2) 0 - Combat:
3) 0 - Items and Equipment:
4) 2 - Story: main story at the forefront; world full of hints and lore;
5) 2 - Exploration: open world from the beginning, visited locations remain open
6) 1 - Quests and Puzzles: side quests not related to the main quest,
Ax Battler was compared to Zelda II at its release; however, Zelda II does quite a bit more. First of all, this game has no experience levels. Beyond health, I'm not sure there are any stats to consider. Combat is action based with options limited to attacking and jumping. With the limited scope, I think the game has more in common with Gargoyle's Quest than Zelda. Towns exist, but don't support the usual stores. They're merely hubs for information on the next dungeon to tackle. There are training houses to gain special abilities like high jumping.
The game has a top-down overworld, random side-scrolling battles, and dungeons that include platforming in the same side-scrolling perspective. I'm not fully sure there are side quests, and no puzzles I saw in the first 15 minutes. Exploration is fairly linear, although I marked it as open in case it opens later. As far as I can tell, there aren't any items or equipment decisions, although upgrades exist.