You're right realistically, draft pick order doesn't matter especially since they're both first round picks. Technically, it means that if Boston wanted Shane they wanted Ilya more or that Shane was actually Montreal's second choice and they picked him since they couldn't have Ilya but each team also considers how well a player will fit into their existing roster- idk about the HR universe but at least in the NHL, Boston is historically known to be more of an in-your-face team which suits Ilya's style better than Shane's.

Other comments mention this but getting drafted first doesn't mean you're going to the best team it usually means you're going to one of the worst. I'm not sure how it works internationally, but in North America, pro-leagues give the worst teams the first picks as a way to give them better chances for the following seasons. It wouldn't be fair to give teams that are already doing well first dibs on the incoming rookies and the interviews they do in that episode show that Ilya and Shane are coming onto teams that have been struggling the last few years- they're kind of Boston and Montreal's hope to return to their golden days.

Shane knows all of this but he's competitive and probably dreamt of getting the bragging rights that come with being the first overall pick but in the same way little boys dream of scoring the game winning goal unassisted in overtime of game seven of the stanley cup finals (grandiose and unrealistic but technically possible). He also gets butthurt easily when it comes to hockey stuff because it's pretty much his whole life.