Here I discuss the romanticism in these stories, which frankly resembles Victorian and Edwardian romanticism in its intensity as well as its manifestation of strong attraction under restraint.
That is, the relationships unapologetically linked physical existence (you are here) to excellence and discipline. The characters pursue an emotional high that far outclasses a thousand platitude-heavy "go-get-em" posters. They fight to win. That fight spills over into the relationship.
The sports romances here are not (necessarily) BL. For the male-male characters, the closer term is shonen.
In Yuri on Ice! Yuri K. and Victor do kiss and exchange rings, but the relationship is so focused on the skater-coach-potential-rival factors--being all-in-one to someone else day-in and day-out--the sexual component would be there whether or not a kiss existed.
In fact, again and again, anime and manga make the point that the rivalry, the push to do better, the high expectations, form a bond that is practically unbreakable and transcend everything else. The bond provokes more than slaps on the back (though those happen too). It provokes intense, unrelenting awareness of the "other."
In fact, rivalry is directly linked to team building. As in Chihayafuru, in Free!, a team is disqualified because it allows a non-team member to participate. In Chihayafuru, Arata joins a team from his past, simply to allow them to play the game they love rather than have to forfeit. In Free! newcomer Rei gives up his place to Rin so he can swim with his prior friends in a relay, which experience helps him get back in touch with what matters to him.
In the end, Rin returns to his school's team. He will be competing against his friends in the future. That's the point. Likewise, while Yuri cheers for his rivals and Chihaya thanks hers, both work to outclass those same people. Yuri's romantic feelings in particular are linked to proving he is worthy of Victor's coaching. He is the only one who deserves Victor's attention.
A romantic subplot is more recognizable in Chihayafuru, but it is again subsumed--in this case--by Chihaya's single-mindedness. She is competing for and against Arata as is Taichi. She doesn't attempt to disentangled her longing for Arata from her love for the game, though it is fairly evident to the viewer that she has conflated the two things.Why shouldn't she? Everybody else does!
In many ways, the relationships in manga and anime sports are not that dissimilar to the relationship between Bourne & Landy or McClane & Gruber: an intense relationship between antagonist and protagonist that draws them closer to each other than to anyone else.