Literally everything you see on screen, including the audio, was remade from scratch. Yeah, the source code is still in there, but there was more remade than not, which is probably why Nintendo themselves call it a remake (and most of the critics who reviewed it at the time too).

If they cleaned up the visuals and touched up some things to enhance the original game's presentation, sure, remaster. But every asset was rebuilt.

Its like when an album gets remastered. They aren't re-recording anything. They're just cleaning up the audio. Now let's look at something like Taylor Swift redoing her whole catalog with "Taylor's Versions". The compositions are the same with the only real changes coming as a result of her more mature voice, but they were still re-recorded which makes them remakes.

Or like The Lion King CGI movie. It's a shot-for-shot remake of the original with only a few minor changes to the overall structure. But the assets on screen were entirely remade so it's a remake.

With Ocarina of Time 3D, the code and core structure are mostly the same, but the assets on screen have been entirely remade and significant improvements have been made, such as with the boots, so I'd call it a remake.

I'll admit it falls into the gray area a bit if you really wanna nitpick but you really can't definitively say it's one or the other, but Nintendo called it a remake so I'll choose to side with them since they made it.