It's a scene that I wish had made it through the final cut anyway, because aside from making it crystal clear Frigga is in her room and projecting to Loki, it's also enlightening re: Frigga and Thor. Who is aware she has these little chats with Loki - and it's made clear Odin is not - and admires her for not giving up on Loki but can't bring himself to continue hoping (given how his attempts in Avengers went, that's not surprising, but Frigga says she didn't love Thor any less while he was banished and in disgrace, and never stopped believing he'd change, so now she's doing the same with Loki). Thor also asks her whether she ever regretted sharing her magic with Loki, and she says no, because "your father and you cast such huge shadows" that she thought giving Loki magic and sharing that with him would compensate. All in all, you get the impression Thor thinks Loki is Frigga's favourite but doesn't doubt she loves him, Thor, as well, so doesn't have the huge issues Loki had about seeing Thor as Odin's favourite long before finding out about his biological nature. Also, at no point in the conversation does Loki not being blood related to them (or an ice giant) even come up; you get the impression it's a complete non-issue to Frigga and Thor, which is why they don't really get that it is a big issue to Loki.