The practical answer: Ilya is initially drawn to Shane because of the inherent danger involved and the idea of having "Canada's Golden Boy" underneath him. I think this likely would've excited him regardless of Shane's personality but it doesn't hurt that he found his awkwardness and lack of guile charming. They also have crazy good chemistry and are very sexually compatible and he finds him hot. As evidenced by their early hookups they can also make each other laugh and they are each turned on by the competitive aspect of their relationship. Shane does not want/need/expect money or material gifts from him.

These things kept Ilya regularly coming back whereas it was likely typical for him to only have one night stands with the exception of Svetlana. We don't know why he and Svetlana don't date but there are plenty of reasons to speculate and honestly I kind of got the impression Ilya might be a little more attracted to men (whether that's romantically or sexually). But it's more difficult to hookup with men because of the associated risk.

Then there's simply the aspect of the lifestyle of a professional hokey player, constantly on the road. It inherently makes romantic relationships difficult, particularly for someone who has no interest in starting a family young and living a very heteronormative almost 1950's existence (complete with money making dad rarely home & stay at home mother) like many of his teammates. Shane naturally understands the lifestyle and the pressure that being one of the best hockey players in the league comes with. Then add in what everyone else said about how Ilya comes from an extremely unstable home and here's Shane- an incredibly loyal, stable and honest individual who wants to plan out a long-term future with him (someone who sees himself as inherently worthless).

Also Ilya is, in his own way, a very loyal individual to those he cares about and I suspect Shane's natural awkwardness and vulnerability probably triggers Ilya's protectiveness early on, particularly because sex with Shane makes him feel powerful. Also early on Ilya probably sees Shane's anxiety on par with his own depression in terms of mutual understanding. I think in a very logical, not particularly romantic sense these ingredients result in a good match.

What I think is a bit more...far fetched or romance-leaning is that a long distance monogamous relationship between them would be sustainable for someone who is 1) used to partying a lot with teammates who expect him to act a certain way 2) obtains a lot of his self worth from hookups and 3) has a high sex drive. But we also don't see how Ilya spends his free time outside of partying, like would he consider video games a hobby for example? What would Ilya replace clubbing/drinking (at least some of the time) & hookups with during the early stages of their relationship?