What is the religious ruling on sexual activity without penetration for a married man?

Your question is unclear whether this woman is your wife or not. If she is your wife, there is no issue, and you are not required to perform ghusl as long as there was no penetration or ejaculation. However, if you ejaculated outside the vagina, then ghusl is required. If she is not your wife, the ruling regarding ghusl does not differ, but you have committed a grave sin by speaking with her and being in seclusion with her. You must repent, seek forgiveness, feel remorse, and abandon association with people like her. You are not subject to a prescribed punishment (hadd) because there was no penetration, but the sin is great, so increase in acts of obedience and voluntary prayers.