Having played literally every canon Zelda game over the course of a year (many for the second or third time) leading up to BotW, I can safely say I never felt like I was not playing a Zelda game.
BotW was different in many ways, but it still had all of the core elements that made it a Zelda game. Many, many puzzles (despite feeling toward the lack of traditional dungeons), exploration, central plot elements, charm, etc. Even acter playing all of the old ones, I still felt this way. With that in mind, I see BotW as a fantastic Zelda game.
If you only played Zelda games to be a dungeon crawler, I van understand how you feel. However as a 30 year Zelda vet (was born the same year Zelda came to the west and started at a very young age), I can tell you that what people consider a Zelda game is subjective.
Some like the exploration and puzzles (BotW had much of this), some play for deeper understandings of the over arching plot (while the plot of BotW was very simple, the lore and history within the game was very deep), and some play for the dungeon crawling experience (this is where BotW fell short).
I am going to assume our OP falls in the later, as if I remember correctly he does not care about the overarching story or timeline, so we can rule that aspect out. Is he wrong? No, absolutely not...is he right though?
Again, not even close. What makes a Zelda game is in the eye of the beholder. While what he may like about past games could be lacking for him, for others (like myself) it had everything it needed to be a true and great Zelda experience. After all, every game plays different in one way or another.
Zelda 1 and BotW were true open world
Zelda 2 was more like a platformer
ALttP, OoT, TP, Minish Cap, Oracle games, and Link's Awakening fall under what most people consider the traditional formula.
Four Swords, Four Swords Adventures, and Triforce Heros all fall under co op experiences.
Wind Waker, Phantom Hourglass, and Spirit Tracks were all games that featured completely new ways to explore the land through boats and trains, and two of then used touch controls.
Skyward Sword featured the concept of having environmental dungeons lead up to the actual dungeons. Many times it fely like you were in a dungeon when you were not.
Majora's Mask had the 3 day system and was Side Quest orientated rather than dungeon orientated, having only four dungeons.
And a Link Between Worlds was a combo of open world and traditional Zelda formulas.
So as you can see, most canon Zelda titles olay different from one another as it is. So what you might perceive as a Zelda game may differ completely from another person's point of view. There is no right or wrong answer in this case, there are points to be made on both sides.
You feel one way, I feel another. That is all there is to it and I understand where you are coming from. Just be aware that not everyone shares the same view on what makes a good or bad Zelda game, as there are just too many factors that go with that.
Just my two rupees.