• bhīṣmaka-sutām — the daughter of Bhīṣmaka
  Bhīṣmaka was Rukmiṇī's father, king of Vidarbha. Vyāsa uses the patronymic to emphasize her royal pedigree — this is no commoner; the marriage is dynastically perfect, even as it was conducted rākṣasa-style.
• vidhi-vat — in accordance with the injunctions of the Vedas
  Vidhi (injunction) + vat (according to). The Bhāgavatam goes out of its way to clarify: although the bride-winning was rākṣasa, the wedding itself was strictly Vedic. The two procedures are distinct. Gauḍīyas insist on this point against later detractors.
• upayeme — He married
  Perfect middle of upa-√yam, 'to take to oneself.' The specific verb for marriage. Cf. its use throughout Yājñavalkya-smṛti. Vyāsa uses the most formal marriage-verb to dignify the rite.
• puram — to His capital
  Dvārakā. Vyāsa never names it here — only 'puram.' The reader supplies the name from context. The verse keeps the bride's arrival luminous and slightly abstract, as if she is entering not a city but a state-of-being.
• kuru-udvaha — O protector of the Kurus
  Vocative addressed to Parīkṣit, the Kuru-line king to whom Śuka tells this. The Bhāgavatam keeps the listener inside the frame. Parīkṣit is reminded he too is part of the same family network that includes the bride's new home.

Having reduced the kings to their cities, the Lord brings the bride to His own city — vidhi-vat, according to the very Vedic injunctions the rākṣasa-vivāha section of the dharma-śāstras explicitly recognizes. The 'abduction' is, in śāstra-eyes, a wedding from start to finish.