I think they've crossed from the fanservice to straight up UST romance.
Like, the heck, if we apply the minimum of Earth reality, there's no other explanation for the character's behavior and there's no person on Earth who wouldn't think they're watching a gay romance. 
This is something a friend and I have been discussing off and on for two weeks now because we feel the same as the bold and the consensus is - we don't know. It's actually somewhat frustrating. On one hand, if this was a het pair, there is no doubt all cues for a romance are being hit. But on the other hand, gay couple?
The truth is, the history of anime is very frustrating here. There are very few that went this way just like that without prior clear intent; No.6 with Nezushi comes to mind but this is in the dystopia, SF genre. Very different.
Fujoshi fanservice is so common though and then, on top of that, it is very common in sports anime in particular. The onsen scenes are very in line with that. They correspond to things from Free to Prince of Stride.
But then, there are other, much more subtle things, that say, no, it's romance. These are different from what is standard and say queer representation instead of queer-baiting. Yuuri and his little arc with eros was very, very interesting for a Japanese anime. I was genuinely taken aback. A man not feeling comfortable with the role of playboy/masculine but instead embracing his feminine side and going with the seduction, a clear statement of who he skates for and Victor responding (this was actually somewhat confirmed by one of the producers of the anime, saying Yuuri stole Victor's heart then), really surprised me. There are other moments that you can glimpse if you know a thing or two about Japan, like Victor taking care of Yuuri's hair for example or the more general ones like the talk on the beach in correspondence with the hug later.
But then again, homosexuality and anime. So genuinely I do not know. That I would say yes, it's romance right away if this were a heterosexual couple and that I still cannot here genuinely sucks for me tbh. I wish we could be past that. But we're not and there's a very real possibility this will end up as simply the biggest queerbaiting anime so far. It's up in the air.
There is a show that surprised me once like this. It's not Japanese though (American) but very, very famous. The Legend of Korra was signaling Korrasami and I remember these same conversations happening. It actually went through with it in the end, which was a massive positive. Who knows? Might happen again. Personally though? I don't think so. Maybe I'm just cynical, and been around for too long, but I don't think so. I don't think they have the guts to go through with it. Please skating gods let me be wrong.
But I guess that won't happen in season 1 for sure.
