Since the manga isn't over, nothing's set in stone, yet. So, I can only give you my assumptions.
I'm actually quite sure that there is or will never be a romantic vibe between Tatara and Shizuku. As Prasanth has already said, Tatara probably never held any romantic feelings for her, but rather admiration and respect.
Moreover, the main heroine actually is Chinatsu and not Shizuku as many might have assumed while watching the first half of the anime. Chinatsu appears in the second half and henceforth always stays in the foreground with Tatara as his main dance partner (Shizuku and Mako were only temporary ones). She simply didn't show up at the very beginning of the story. That's why I'm very confident to say that the romance tag refers to the relationship between Tatara and Chinatsu.
The story focuses mainly on the character development of and the relationship btw. these two protagonists. "After a difficult start because of their totally different personalities and background, Chinatsu and Tatara slowly find themselves on the same wavelength and steadily grow together as dance partners and reach new heights." That's probably a suitable synopsis of their relationship.
Btw., there has been quite a few hints in the anime that this relationship is slowly progressing in a romantic way. So, if you want to ship Tatara with Shizuku, then you'll most likely be disappointed (Shizuku's romantic relationship also probably revolves around her main dance partner Kiyoharu).
I personally am more than satisfied with the relationship btw. our two protagonists and I really want to encourage you not to give up watching this anime only because you initially shipped Tatara with Shizuku. I'm quite sure that you will change your mind as the story progresses.