• priyā-juṣṭe paryaṅke — on the bed used by His beloved
  priyā (beloved) + juṣṭe (used, frequented) + paryaṅka (bed). The most intimate piece of furniture in Bhagavān's palace, and Sudāmā was seated there. The poet records the violation of every protocol of distance.
• bhrātaraḥ yathā — just as (one of His) brothers
  bhrātṛ (brother) + yathā (as). Sudāmā was treated as a brother. In Vraja he had been treated as a sakhā at the ashram; in Dvārakā, the same Bhagavān upgrades nothing — Kṛṣṇa keeps the rasa.
• mahiṣyā vījitaḥ — fanned by His queen
  mahiṣī (queen) + vījita (fanned). The queen of the world's wealthiest king personally fanned the brāhmaṇa in rags. The whole chapter's claim about brahmaṇyatā is condensed in this one detail.
• śrāntaḥ — tired
  Past participle of √śram (to be tired). Sudāmā walked to Dvārakā on foot through forests; his body was actually tired. The Bhāgavatam never aestheticizes him into a yogi — he is a tired pedestrian whom Kṛṣṇa's queen attends to.
• bāla-vyajana-hastayā — in whose hand was a yak-tail fan
  Compound: bāla (hair, here yak-tail) + vyajana (fan) + hasta (hand). The cāmara is one of the standard items in temple deity worship — and here it is in Rukmiṇī's hand, used on Sudāmā. The poet inverts the directionality of ritual.

A king's only brother arrives travel-worn, and the queen herself takes up the cāmara to fan him. Sudāmā's wonder is not at the throne-room but at this: Rukmiṇī fanned me. The queen's own hand became service to the brāhmaṇa's tiredness — because the king saw him as His own.