• raṅga - madhye — within the wrestling arena
  Compound: raṅga (arena) + madhye (within). The Mathurā stage of SB 10.44. The verse names the place to remind Nanda: the work was done in public view, witnesses exist, the deed is verified.
• satyam-karoti — He will make true
  Compound verb: satyam (true) + √kṛ (to make). The Sanskrit idiom for fulfilling a promise — 'to make-true the word.' Gauḍīya kīrtana tradition uses this same phrase in songs of bhakti-saṅkalpa: the Lord's word is what becomes truth.
• samāgatya — by coming back
  Gerund of sam-ā-√gam (to come together / return). The chapter's vocabulary of return — āgamiṣyati (34), samāgatya (35) — repeats and reinforces. Uddhava is saying the same thing in adjacent forms, the way a parent reassures a child.
• pratīpam — the enemy
  Accusative of pratīpa — the contrary one, the opposed. Kaṁsa is named not by his throne but by his moral position — opposed to the Yadus. Gauḍīya theology of bhakti-vighna: the enemy is defined relationally, by his stance against the Lord's family.
• sarva - sātvatām — of all the Yadus
  Compound: sarva (all) + sātvata. The Sātvatas as the Yadu-Vaiṣṇavas; the term will later become a sect-name for Pāñcarātrika devotees. The verse counts Nanda's family among the sātvatas Kṛṣṇa protects.
• vaḥ — to you
  Enclitic pronoun, plural-genitive. Uddhava addresses Nanda and Yaśodā together — and beyond them, the gopīs and the village. The 'you' is wider than the conversation. Vraja receives the promise, not only its parents.

Uddhava reminds them: 'Having killed Kaṁsa, He will keep His word.' The argument is from action already taken — the bigger task (Kaṁsa) is done; the smaller (return) will not be neglected. Bhakti's logic: take confidence from what He has already finished.