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"Therefore," Ayumu paused for breath. "Tachihara Reika, do you attest to being Ketsurui Kotori's consort and to be responsible for her as her legal guardian?"
Reika's a consort for Kotori, not a full-blown marriage partner. Unfortunately, I don't think that comes with a ceremony
Think more along the lines of Lady Jessica being the bound concubine of Duke Leto Atreides in the Dune series; they could have offspring together and their child Paul was even recognised as the legal heir to the Duke, but Leto still had the option of marrying to a partner from a noble house if it ever seemed politically wise to do so.
Likewise, the princess Kotori still has the option of taking another as a full marriage partner or even additional consorts if it suits her fancy -- or like Leto in Dune she can just treat Reika as her wife in every practical way, despite that technically not being the case, while never taking on a full marriage partner.