• arājake — when there was an irregular government
  A (not) + rājaka (kingly rule). Bhāgavatam treats arājakatā as the condition that calls Bhagavān into history. BG 4.7-8 (yadā yadā hi dharmasya) is the doctrinal parallel — He descends to restore the broken order.
• sādhavaḥ — those who were honest
  Sādhus — the saintly, the devoted. Their protection is the explicit cause of avatāra (paritrāṇāya sādhūnām, BG 4.8). Garga names the recipients of Kṛṣṇa's prior interventions so Nanda hears himself included.
• dasyu-pīḍitāḥ — being disturbed by rogues and thieves
  Dasyu (rogue) + pīḍita (oppressed). The dasyus prefigure the asuras Kṛṣṇa has been killing this very chapter — Pūtanā, Tṛṇāvarta, Baka, Vatsa, Dhenuka, Pralamba, Kāliya. The pattern is one pattern.
• rakṣyamāṇāḥ — were protected
  Present passive participle of √rakṣ — to protect. Rakṣaṇa is the avatāra's signature; Govardhana itself is rakṣaṇa-līlā par excellence. Garga is saying: this is what He does.
• vraja-pate — O King of Vraja
  Vraja + pati (lord). Garga calls Nanda the king of Vraja while explaining that the King of all worlds has come to his household. The political and the cosmic are layered in one address.

When the watchman is asleep and the village gates hang open and bandits come every evening, sometimes a stranger arrives, settles among the villagers, and within a season the bandits are gone — not because he announced himself but because his being there altered the air. Garga is telling Nanda that this same Person has come to Vraja before, in other roles.