The DNA finding establishes biological sex: two X chromosomes, no Y chromosome. This is a finding about the individual’s chromosomal profile, not a complete description of their identity or social position.
Social gender — how a person was understood within their community, what roles they occupied, how they understood themselves — is not accessible through chromosomal analysis. It is not directly accessible through burial goods either, though burial goods can provide evidence about how a community chose to represent an individual at death.
Neil Price, in the coverage of the 2019 paper, described “a broad spectrum of possibilities” for how this individual might have understood their own identity. He noted that the modern term “transgender” may be an inadequate and anachronistic category for a person who lived in the Viking Age, but he also noted that Viking Age culture appears to have recognized categories of gender identity and sexual identity that did not map neatly onto a simple male/female binary. The Norse literary and mythological tradition contains figures whose gender and sexuality are complex, and there is scholarly work on gender fluidity in Viking Age contexts.
The researchers explicitly rejected importing modern categorical frameworks as known historical facts. The person in grave Bj 581 lived in the Viking Age. The categories through which they understood themselves, and through which their community understood them, were Viking Age categories — not twenty-first century ones.
What can be said: this individual was buried with the full assemblage of a high-status warrior burial. The community or family that buried them chose that assemblage. The biological sex of the individual does not conform to the assumption that had governed the interpretation of the grave for 130 years. The exact meaning of these facts for this individual’s lived identity is not determinable from the available evidence.