Why don't you think it qualifies? You have an inventory, you have money and buy items, you advance your character (not through experience points, but through finding secrets and beating major enemies).
You don't really make choices in most Zelda game. All the character advancement is coupled to story progression (you get an item in the 1st dungeon that lets you access the 2nd dungeon and so on). I think that reduces the "role playing" that goes on and makes Zelda more of an Action/Adventure series.
It's not even true for many of the "classic" Zelda games like Link to the Past or Ocarina of Time. Sure, there's a series of mandatory quests with associated items -- but there's also a bunch of side quests to pick up optional items, like extra heart containers, additional bottles, and various tools (like the Cape of Byrna in LttP or the masks in OoT).
Those numbers are important! In classic rpgs, both western and Japanese, skillful play consists in strategically manipulating those numbers to defeat challenges. It's a very different feeling than in an action game where skillful play is about manipulating the virtual physics of your avatar.
Paper Mario is clearly an RPG, but it has a similar amount of numbers backing it's system as your average Zelda. It's just that Zelda hides the numbers from you and Paper Mario does not.
A good way of thinking about this is that the Zelda games are genetically rpgs, in the sense that Miyamoto was doing his spin on the style of game that Nihon Falcom had introduced. Obviously, the absense of numerical character abilities in LoZ makes it feel somewhat different than quintessential Japanese ARPGs like YS or Seiken Denetsu (Legend of Mana).
