What is my duty concerning a young woman whom I saw speaking to a young man in an electronic game, then informed about her, and now fear that I may have wronged her?

What you have done by having ill thoughts about people and accusing them of shameful things without proof is a reprehensible act. The duty is to assume their good intentions until proven otherwise, as Allah Almighty says: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." You must hasten to repent. As for this girl, it is sufficient to supplicate for her and mention her kindly, as this is one of the moral rights.